This Life lexicon is compiled by Stephen A. Silver from various sources
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See Demonoid.
Found by Achim Flammenkamp in August 1994. The name was suggested by Bill Gosper, noting that the phase shown below displays the period in binary.
See Demonoid.
A spaceship discovered by Dean Hickerson in December 1989, the first spaceship of its kind to be found. Hickerson then found a small tagalong for this spaceship which could be attached to one side or both. These three variants of 119P4H1V0 were the only known c/4 orthogonal spaceships until July 1992 when Hartmut Holzwart discovered a larger spaceship, 163P4H1V0.
Found by Dave Buckingham, August 1972. This is one of only three essentially different p3 oscillators with only three cells in the rotor. The others are stillater and cuphook.
See also Achim's p4.
The following converter, discovered by Matthias Merzenich in July 2013. It accepts an MWSS as input, and produces an output glider travelling at a 135-degree angle relative to the input direction.
A spaceship travelling at seventeen forty-fifths of the speed of light. This was the first known macro-spaceship speed. See Caterpillar for details.
The only other two-glider collision besides the standard kickback that produces a clean output glider with no leftover ash. The 180-degree change in direction is occasionally useful in glider synthesis, but is rarely used in signal circuitry or in self-supporting patterns like the Caterpillar or Centipede, because 90-degree collisions are generally much easier to arrange.
See seed.
A knightship that travels obliquely at the fastest possible speed. To date the only known example of a spaceship with this velocity is Sir Robin.
The following glider-supported Herschel climber reaction used in the self-supporting waterbear knightship, which can be repeated every 79 ticks, moving the Herschel 23 cells to the right and 5 cells upward, and releasing two gliders to the northwest and southwest. As the diagram shows, it is possible to substitute a loaf or other still lifes for some or all of the support gliders. This fact is used to advantage at the front end of the waterbear.
c;79_Herschel_climber.png)
A 39786×143 quadratic growth pattern found by Michael Simkin in October 2014, two days after 25-cell quadratic growth and a week before switch-engine ping-pong.
A 25-cell quadratic growth pattern found by Michael Simkin in October 2014, with a bounding box of 21372×172. It was the smallest-population quadratic growth pattern for two days, until the discovery of 24-cell quadratic growth. It superseded wedge, which had held the record for eight years. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
A spaceship discovered by Dean Hickerson in August 1989. It was the first c/3 spaceship to be discovered. In terms of its 25 cells, it is tied with 25P3H1V0.2 as the smallest c/3 spaceship. Unlike 25P3H1V0.2, it has a population of 25 in all of its phases, as well as a smaller bounding box.
A spaceship discovered by David Bell in early 1992, with a minimum of 25 cells - the lowest number of cells known for any c/3 spaceship. A note in Spaceships in Conway's Life indicates that it was found with a search that limited the number of live cells in each column, and possibly also the maximum cross-section (4 cells in this case). See also edge-repair spaceship for a very similar c/3 spaceship with a minimum population of 26.
= wedge.
The first spaceship of its type to be discovered, found by Jason Summers on 22 November 2000.
Two thirds of the speed of light - the speed of signals in a 2c/3 wire or of some against the grain negative spaceship signals in the zebra stripes agar, and also the speed of burning of the blinker fuse and the bi-block fuse.
A wire discovered by Dean Hickerson in March 1997, using his dr search program. It supports signals that travel through the wire diagonally at two thirds of the speed of light.
Each 2c/3 signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.
Considerable effort has been spent on finding a way to turn a 2c/3 signal 90 or 180 degrees, since this would by one way to prove Life to be omniperiodic. There is a known 2c/3 converter shown under signal elbow, which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it can't be used to complete a loop.
Noam Elkies discovered a glider synthesis of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See stable pseudo-Heisenburp for details. On 11 September 2017, Martin Grant reduced the input reaction to five gliders, or three gliders plus a Herschel. With the Herschel option the recovery time is 152 ticks.
See also 5c/9 wire.
A spaceship travelling at two fifths of the speed of light. The only such spaceships that are currently known travel orthogonally. Examples include 30P5H2V0, 44P5H2V0, 60P5H2V0, and 70P5H2V0. As of June 2018, only 30P5H2V0 and 60P5H2V0 have known glider synthesis recipes.
A spaceship travelling at two sevenths of the speed of light. The only such spaceships that are currently known travel orthogonally. The first to be found was the weekender, found by David Eppstein in January 2000. See also weekender distaff.
The smallest known Cordership, with a minimum population of 100 cells, discovered by Aidan F. Pierce on 31 December 2017. Luka Okanishi produced a 9-glider synthesis of the spaceship on the same day.
Two gliders can react with each other in many different ways, either at right angles, or else head-on. A large number of the reactions cleanly destroy both gliders leaving nothing. Many of the remaining reactions cleanly create some common objects, and so are used as the first steps in glider synthesis or as part of constructing interesting objects using rakes. Only a small number of collisions can be considered dirty due to creating multiple objects or a mess.
Here is a list of the possible results along with how many different ways they can occur (ignoring reflections and rotations).
------------------------------- result right-angle head-on ------------------------------- nothing 11 17 beehive 1 0 B-heptomino 1 2 bi-block 1 0 blinker 2 1 block 3 3 boat 0 1 eater1 1 0 glider 1 1 honey farm 3 2 interchange 1 0 loaf 0 1 lumps of muck 1 0 octomino 0 1 pi-heptomino 2 1 pond 1 1 teardrop 1 0 traffic light 2 1 four skewed blocks 0 1 dirty 6 0 -------------------------------The messiest of the two-glider collisions in the "dirty" category is 2-glider mess.
A constellation made up of eight blinkers, four blocks, a beehive and a ship, plus four emitted gliders, created by the following 2-glider collision.
A spaceship discovered by Paul Tooke on 7 December 2000. With just 30 cells, it is currently the smallest known 2c/5 spaceship. A glider synthesis for 30P5H2V0 was found by Martin Grant in January 2015, based on a predecessor by Tanner Jacobi.
The rate of travel of the 31c/240 Herschel-pair climber reaction, and Caterpillar-type spaceships based on that reaction. Each Herschel travels 31 cells orthogonally every 240 ticks.
The mechanism defining the rate of travel of the Centipede and shield bug spaceships. Compare pi climber. It consists of a pair of Herschels climbing two parallel chains of blocks. Certain spacings between the block chains allow gliders from each Herschel to delete the extra ash objects produced by the other Herschel. Two more gliders escape, one to each side, leaving only an exact copy of the original block chains, but shifted forward by 9 cells:
A spaceship travelling at three sevenths of the speed of light. The only such spaceships that are currently known travel orthogonally. The first to be found was the spaghetti monster, found by Tim Coe in June 2016.
See Cordership.
A spaceship discovered by Dean Hickerson on 23 July 1991, the first 2c/5 spaceship to be found. Small tagalongs were found by Robert Wainwright and David Bell that allowed the creation of arbitrarily large 2c/5 spaceships. These were the only known 2c/5 spaceships until the discovery of 70P5H2V0 in December 1992.
The following small converter, which accepts an MWSS or LWSS as input and produces an output glider travelling at a 45-degree angle relative to the input direction.
The following pure glider generator.
= Fast Forward Force Field. This term is no longer in common use.
A reaction involving 4 gliders which cleanly produces 5 gliders. The one shown below was found by Dieter Leithner in July 1992:
The first two gliders collide to produce a traffic light and glider. The other two gliders react symmetrically with the evolving traffic light to form four gliders. A glider gun can be built by using reflectors to turn four of the output gliders so that they repeat the reaction.
A 56-cell spaceship discovered by Hartmut Holzwart in 2009, the smallest known c/6 orthogonal spaceship as of July 2018.
A spaceship discovered by Matthias Merzenich on 5 September 2010. In terms of its minimum population of 58 cells it is the smallest known c/5 diagonal spaceship. It provides sparks at its trailing edge which can perturb gliders, and this property was used to create the first c/5 diagonal puffers. These sparks also allow the attachment of tagalongs which was used to create the first c/5 diagonal wickstretcher in January 2011.
A wire discovered by Dean Hickerson in April 1997, using his dr search program. It supports signals that travel through the wire diagonally at five ninths of the speed of light. See also 2c/3 wire.
Found by Dave Greene, 1 November 2004, based on 92P156.
A 60-cell spaceship discovered by Tim Coe in May 1996. It was the first non-c/2 orthogonal spaceship to be successfully constructed via glider synthesis.
A spaceship discovered by Nicolay Beluchenko in July 2006. It was the smallest known c/5 diagonal spaceship until the discovery of 58P5H1V1 in September 2010.
A spaceship discovered by Hartmut Holzwart on 5 December 1992.
A high-clearance eater5 variant that can suppress passing gliders in tight spaces, such as on the inside corner of an R64 Herschel conduit. Like the eater5 and sidesnagger, the 7×9 eater is able to eat gliders coming from two directions, though this ability is not commonly used.
= lobster
A spaceship discovered by Jason Summers on January 8, 2005. It was the smallest known c/5 diagonal spaceship until the discovery of 67P5H1V1 in July 2006.
See kickback reaction.
Discovered by Jason Summers on October 31, 2004. It is actually an eight-barrel glider gun, with all output gliders suppressed by eater1s. Replacing each pair of eater1s with a beehive doubles the period and produces 60P312.
Separated by 9 half diagonals. Specifically used to describe the distance between the two construction lanes in the linear propagator.
on a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean Hickerson reduced it to a finite form using figure-8s the same day. The neater finite form shown here, replacing the figure-8s with blocks, was found by David Bell in August 1994. See factory for a use of this oscillator.
Found by Achim Flammenkamp, July 1994.
Dave Buckingham found this in a less compact form (using two halves of sombreros) in 1976. The form shown here was found by Achim Flammenkamp in 1988. The rotor is two copies of the rotor of 1-2-3-4, so the oscillator is sometimes called the "dual 1-2-3-4".
Found by Achim Flammenkamp, July 1994.
A methuselah found by Charles Corderman. It has a final population of 633 and covers an area of 215 by 168 cells, not counting the 13 gliders it produces. Its ash consists of typical stable objects and blinkers, along with the relatively rare mango and a temporary eater1.
Found by Dean Hickerson in March 1993.
A term used for negative spaceships travelling in zebra stripes agar, perpendicular to the stripes, and also for against-the-grain grey ships.
Below is a sample signal, found by Hartmut Holzwart in April 2006, that travels against the grain at 2c/3. This "negative spaceship" travels upward and will quickly reach the edge of the finite patch of stabilized agar shown here.
Holzwart proved in 2006 that 2c/3 is the maximum speed at which signals can move non-destructively against the grain through zebra stripes agar.
A grey ship in which the region of density 1/2 consists of lines of ON cells lying perpendicular to the direction in which the spaceship moves. See also with-the-grain grey ship.
Any pattern covering the whole plane that is periodic in both space and time. The simplest (nonempty) agar is the stable one extended by the known spacefillers. For some more examples see chicken wire, houndstooth agar, onion rings, squaredance and Venetian blinds. Tiling the plane with the pattern O......O produces another interesting example: a p6 agar which has a phase of density 3/4, which is the highest yet obtained for any phase of an oscillating pattern. See lone dot agar for an agar composed of isolated cells.
This is the smallest still life that has more than one island.
Found by Dave Buckingham in 1972. The rotor consists of two copies of that used in the burloaferimeter.
The following reaction (found by Rich Schroeppel and Dave Buckingham) in which a honey farm predecessor, catalysed by an eater and a block, reappears at another location 47 generations later, having produced a glider and a traffic light. This was in 1990 the basis for the Dean Hickerson's construction of the first true p94 gun, and for a very small (but pseudo) p94 glider gun found by Paul Callahan in July 1994. (The original true p94 gun was enormous, and has now been superseded by comparatively small Herschel loop guns and Mike Playle's tiny AK94 gun.)
The smallest known gun using the AK47 reaction, found by Mike Playle in May 2013 using his Bellman program.
= Jolson
A promising partial result discovered by Eugene Langvagen in March 2004. This was an early near miss in the ongoing search for a small elementary (2,1)c/6 knightship. After six generations, only two cells are incorrect.
Found in 1971.
A type of Herschel transceiver where the receiver can be used in either of two mirror-image orientations. See also chirality.
A pattern that consumes ants. Matthias Merzenich discovered a c/5 anteater on 15 April 2011. See wavestretcher for details.
The standard form is shown below. It is also possible for any ant to be displaced by one or two cells relative to either or both of its neighbouring ants. Dean Hickerson found fenceposts for both ends of this wick in October 1992 and February 1993. See electric fence, and also wickstretcher.
Any wickstretcher or wavestretcher that stretches ants. Nicolay Beluchenko and Hartmut Holzwart constructed the following small extensible antstretcher in January 2006:
The following induction coil.
See apgsearch
See apgsearch.
See apgsearch.
One of several versions of a client-side Ash Pattern Generator soup search script by Adam P. Goucher, for use with Conway's Life and a wide variety of other rules. Development of the original Golly-based Python script started in August 2014. After the addition in 2016 of apgnano (native C++) and apgmera (self-modifying, 256-bit SIMD compatibility), development continues in 2017 with apgluxe (Larger Than Life and Generations rules, more soup shapes). Several customized variants of the Python script have also been created by other programmers, to perform types of searches not supported by Goucher's original apgsearch 1.×.
All of these versions of the search utility work with a "haul" that usually consists of many thousands or millions of random soup patterns. Each soup is run to stability, and detailed object census results are reported to Catagolue. For any rare objects discovered in the ash, the source soup can be easily retrieved from the Catagolue server.
An asymmetric PPS. The same as the SPPS, but with the two halves 15 generations out of phase with one another. Found by Alan Hensel in May 1998.
A pair of mutually stabilizing switch engines. The archetype is Noah's ark. The diagram below shows an ark found by Nick Gotts that takes until generation 736692 to stabilize, and can therefore be considered as a methuselah.
A long extension, sometimes also called a "wing", hanging off from the main body of a spaceship or puffer perpendicular to the direction of travel. For example, here is a sparking c/3 spaceship which contains two arms.
For an alternate meaning see construction arm.
A method of generating slow salvos across a wide range of lanes without using a construction arm with a movable elbow. Instead, streams of gliders on two fixed opposing lanes collide with each other to produce clean 90-degree output gliders. Slowing down one of the streams by 8N ticks will move the output lanes of the gliders toward the source of that stream by N full diagonals. This construction method was used to create the supporting slow salvos in the half-baked knightships, and also in the Parallel HBK gun.
The stable or oscillating objects left behind when a chaotic reaction stabilizes, or "burns out". Experiments show that for random soups with moderate initial densities (say 0.25 to 0.5) the resulting ash has a density of about 0.0287. (This is, of course, based on what happens in finite fields. In infinite fields the situation may conceivably be different in the long run because of the effect of certain initially very rare objects such as replicators.)
Indicates that precise relative timing is not needed for two or more input signals entering a circuit, or two or more sets of gliders participating in a glider synthesis. In some cases the signals or sets of gliders can arrive in any order at all - i.e., they have non-overlapping effects.
However, in some cases such as slow salvo constructions, there is a required order for some of the incoming signals. These signals can still be referred to as "asynchronous" because the number of ticks between them is infinitely adjustable: arbitrarily long delays can be added with no change to the final result. Compare synchronized.
Found by Dave Buckingham, 1973. The average number of live rotor cells is five (V), which is also the period.
The following spaceship, found by Hartmut Holzwart in April 2004. A glider synthesis of this spaceship was completed by Tanner Jacobi in April 2015.
The following p104 double-barrelled glider gun. It uses a B-heptomino and emits one glider every 52 generations. It was found by Noam Elkies in March 1996, except that Elkies used blockers instead of molds, the improvement being found by David Bell later the same month.
A Herschel conduit discovered by Michael Simkin in 2015 using his search program, CatForce. It is one of two known Blockic elementary conduits. After 60 ticks, it produces a Herschel rotated 180 degrees at (-6,-10) relative to the input. It can most easily be connected to another B60 conduit, producing a closed loop, the Simkin glider gun.
Any oscillator whose rotor consists of a string of cells each of which is adjacent to exactly two other rotor cells, except for the endpoints which are adjacent to only one other rotor cell. Compare muttering moat. Examples include the beacon, the great on-off, the light bulb and the spark coil. The following less trivial example (by Dean Hickerson, August 1997) is the only one known with more than four cells in its rotor. It is p4 and has a 6-cell rotor.
Another term for a backwards rake. A p8 example by Jason Summers is shown below. See total aperiodic for a p12 example.
A glider which moves at least partly in the opposite direction to the puffer(s) or spaceship(s) under consideration.
An object in a converter, usually a small still life, that is temporarily destroyed by an incoming signal, but in such a way that a usable output signal is produced. In general such a converter produces multiple output signals (or a signal splitter is added) and one branch of the output is routed to a factory mechanism that rebuilds the bait object so that the converter can be re-used.
A fuse by Keith McClelland.
A loaf hassled by two blocks and two caterers. The original form (using p4 and p6 oscillators to do the hassling) was found by Robert Wainwright in August 1989.
A common formation of two bi-loaves.
A common three-bit polyplet spark used in glider synthesis and signal circuitry. The buckaroo is an oscillator that produces this spark. It can be used to turn a glider 90 degrees:
Any p2 oscillator in the infinite sequence bipole, tripole, quadpole, pentapole, hexapole, heptapole ... (It wasn't my idea to suddenly change from Latin to Greek.) This sequence of oscillators was found by the MIT group in 1970. The term is also used (usually in the form "barber pole") to describe other extensible sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection. Any barberpole can be lengthened by the reaction shown in barbershop. See also pseudo-barberpole.
= quad
An object created by Jason Summers in 1999 which builds an infinite barberpole. It uses slide guns to repeatedly lengthen a barberpole at a speed of c/124. The key lengthening reaction from Mark Niemiec is shown below:
The third most common oscillator. Found by Conway, March 1970.
The second most common still life.
A Spartan logic circuit discovered by Tanner Jacobi on 12 May 2015. It converts an input glider signal into a beehive, in such a way that the beehive can cleanly absorb a single glider from a perpendicular glider stream. The circuit can't be re-used until the beehive "bit" is cleared by the passage of at least one perpendicular input.
This term has sometimes been used for the beehive catalyst variant of SW-2, and also for Paul Callahan's larger glider stopper, which also provides optional 0-degree and 180-degree glider outputs.
See lightspeed wire.
A program for searching catalytic reactions, developed by Mike Playle, which successfully found the Snark.
The spark of a MWSS or HWSS other than the tail spark.
Found by Nicolay Beluchenko on April 14, 2009. It was the first period 37 oscillator to be found, and remains the smallest.
Found by Nicolay Beluchenko on February 17, 2009. It was the first non-trivial period 51 oscillator to be found.
Found by Dean Hickerson, August 1989. See also odd keys and short keys.
One of the earliest and most remarkable converters, discovered by Dave Buckingham in July 1996. In 59 generations it transforms a B-heptomino into a clean Herschel with very good clearance, allowing easy connections to other conduits. It forms the final stage of many of the known composite conduits, including the majority of the original sixteen Herschel conduits. Here a ghost Herschel marks the output location:
This is a very common methuselah that evolves into three blocks, two gliders and a ship after 148 generations. Compare with Herschel, which appears at generation 20 of the B-heptomino's evolution. B-heptominoes acquired particular importance in 1996 due to Dave Buckingham's work on B tracks. See in particular My Experience with B-heptominos in Oscillators.
This pattern often arises with the cell at top left shifted one space to the left, producing a seven-bit polyplet that shares the same eight-bit descendant but is not technically a heptomino at all. This alternate form is shown as the input for elementary converter patterns such as BFx59H and BRx46B. This is standard practice for elementary conduits, since many of these conduits do in fact produce this alternate form as output.
The B-heptomino is considered a failed puffer or failed spaceship, since on its own it travels at c/2 for only a short time before being affected by its own trailing debris. However, it can be stabilized into a c/2 puffer or into a clean c/2 rake or spaceship. See, e.g., ecologist.
The smallest pseudo still life.
A clean fuse made by a row of bi-blocks separated by 2 cell gaps. The bi-block row wick is usually created by a bi-block puffer. The burning advances 8 cells every 12 generations making its speed 2c/3.
Any puffer whose output is bi-blocks. The term is particularly used for p8 c/2 puffers, in which case a bi-block fuse is created. A bi-block puffer is easily made using two backrakes whose gliders impact symmetrically. Jason Summers welded two backrakes to form a more compact puffer, as shown below.
= boat-tie
The following pure glider generator consisting of two clocks.
= figure-8
= HWSS
This was found by Dean Hickerson in December 1989 and was the first known diagonal spaceship other than the glider.
= dock
Any oscillator in which the rotor is enclosed within the stator. Examples include airforce, cauldron, clock II, Hertz oscillator, negentropy, pinwheel, pressure cooker and scrubber.
This term has been used in at least three different senses. A bi-loaf can be half a bakery:
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The barberpole of length 2.
= ship-tie
A Spartan memory cell found by Paul Callahan in 1994. It can be in one of two states, containing either a boat or a block. Input gliders on the appropriate paths can change the boat to a block, or vice-versa, while also emitting an output glider. Unlike many memory cells, attempts to change the state to the one it is already in are ignored with the glider passing through with no reaction. This makes it easy to reset the memory cell to a known state. Which of the two states is considered the SET and which considered the RESET is just a matter of convention.
The pattern below shows the "boat" state of the memory cell in its original 1994 form. Two gliders are also shown to indicate the input paths used to change the states. A smaller version is shown under century eater, with the circuit in its "block" state.
As shown, the rightmost glider changes the state from a boat to a block and emits a glider to the upper right, while the leftmost glider passes through unchanged. Alternatively, when the state contains a block, then the leftmost glider changes the state from a block to a boat, and emits a glider to the lower right, while the rightmost glider passes through unchanged.
A live cell, if used in reference to still life population. For example, a beehive is a 6-bit still life. Other uses generally involve information storage: a memory cell such as a honey bit that can hold one binary bit of information for later retrieval.
Found by Peter Raynham, July 1972.
. A term used at MIT and still occasionally encountered.
The smallest and most common oscillator. Found by Conway, March 1970.
A clean fuse made from a row of blinkers separated by one cell gaps. The blinker row wick is usually created by a blinker puffer. The fuse can burn in at least three different ways at a speed of 2c/3 depending on the method used to ignite the end of the row of blinkers. This variant has found the most use. The burning advances 12 cells every 18 generations.
Any puffer whose output is blinkers. However, the term is particularly used for p8 c/2 puffers. The first such blinker puffer was found by Robert Wainwright in 1984, and was unexpectedly simple:
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The following glider/blinker collision, which moves a blinker (-1,3) toward the glider source:
Found by Robert Wainwright, June 1977.
A growing spaceship in which the wick consists of a line of blinkers. An example by Paul Schick based on his Schick engine is shown below. Here the front part is p12 and moves at c/2, while the back part is p26 and moves at 6c/13. Every 156 generations 13 blinkers are created and 12 are destroyed, so the wick becomes one blinker longer.
The most common still life, and also the most common object produced by 2-glider collisions (six different ways).
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A common formation of four blocks. The final form of lumps of muck.
Found by Robert Wainwright. See also filter.
Any factory circuit that produces a block in response to an input signal. For a useful high-clearance example see keeper.
Adjective for constellations consisting entirely of blocks. It's possible to arrange blocks in a way that can be triggered by a single glider to produce any glider constructible pattern. A simple example of a Blockic pattern is shown under fuse. See also seed.
See keeper.
The following glider/block collision, which moves a block (2,1) toward the glider source. Performing this reaction twice using a salvo of two gliders can move a block diagonally back by three cells, which can be of use for a sliding block memory.
A pattern emitting streams of gliders which can repeatedly push a block further away. This can be used as part of a sliding block memory.
The following pattern, in which three gliders push a block one cell diagonally, is an example of how a block pusher works.
A universal construction elbow recipe library is also likely to contain one or more block-pushing reactions, since blocks are commonly used as elbows.
The following methuselah, found by Dean Hickerson in July 2002.
A block or a blinker. This term is mainly used in the context of sparse Life and was coined by Rich Schroeppel in September 1992.
The following oscillator, found by Nicolay Beluchenko in April 2004.
A B-heptomino to glider converter found by Tanner Jacobi on 26 May 2016. This converter has the unusual property of being an edge shooter where no part of the reaction's envelope extends beyond the glider's output lane. It can be easily connected to Herschel circuitry via HFx58B or other known elementary conduits.
The only 5-cell still life.
A binary digit represented by the presence of a boat next to a snake (or other suitable object, such as an aircraft carrier). The bit can be toggled by a glider travelling along a certain path. A correctly timed glider on a crossing path can detect whether the transition was from 1 to 0 (in which case the crossing glider is deleted) or from 0 to 1 (in which case it passes unharmed). Three gliders therefore suffice for a non-destructive read. The mechanisms involved are shown in the diagram below. Here the bit is shown in state 0. It is about to be set to 1 and then switched back to 0 again. The first crossing glider will survive, but the second will be destroyed.
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In January 1997 David Bell found a method of reading the bit while setting it to 0. A MWSS is fired at the boat-bit. If it is already 0 (absent) then the MWSS passes unharmed, but if it is 1 (present) then the boat and the MWSS are destroyed and, with the help of an eater1, converted into a glider which travels back along exactly the same path that is used by the gliders that toggle the boat-bit.
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= boat-tie
See tubstretcher.
A 10-cell still life consisting of two boats placed tip-to-tip. The name is a pun on "bow tie".
Dave Greene's name for the following 180-degree glider reflector which he found in April 2001, winning $100 bounties offered by Alan Hensel and Dieter Leithner. The name is taken from Lewis Carroll's _The Hunting of the Snark_, referring to the fact that a small 90-degree stable reflector was really what was wanted. 180-degree reflectors are relatively undesirable and have limited use in larger circuitry constructions.
The boojum reflector was the smallest and fastest known stable reflector until the discovery of the rectifier in 2009, followed by the Snark in 2013.
The following induction coil. It is generation 1 of century.
Found by Dave Buckingham, 1972.
Found by Achim Flammenkamp in August 1994. The name is a back-formation from ship in a bottle.
A label used for the small periodic colour-changing glider reflectors discovered mainly by Noam Elkies in the late 1990s. See p5 bouncer, p6 bouncer, p7 bouncer, p8 bouncer, or p15 bouncer.
The smallest rectangular array of cells that contains the whole of a given pattern. For oscillators and guns this usually is meant to include all phases of the pattern, but in the case of guns, the outgoing stream(s) are excluded. The bounding box is one of the standard ways to measure the size of an object; the other standard metric is the population.
= boat-tie
Found by David Bell, May 1992.
An extensible spaceship containing components which can be attached in multiple ways so that the result can contain arbitrarily many arms arranged like a binary tree. Here is an example of a period 2 c/2 branching spaceship, which also includes a wicktrailer:
Any pattern whose population grows at a quadratic rate, although it is usual to exclude spacefillers. It is easy to see that this is the fastest possible growth rate.
The term is also sometimes used to mean specifically the breeder created by Bill Gosper's group at MIT, which was the first known pattern exhibiting superlinear growth.
There are four common types of breeder, known as MMM, MMS, MSM and SMM (where M=moving and S=stationary). Typically an MMM breeder is a rake puffer, an MMS breeder is a puffer producing puffers which produce stationary objects (still lifes and/or oscillators), an MSM breeder is a gun puffer and an SMM breeder is a rake gun. There are, however, less obvious variants of these types. Other less common breeder categories (SSS, hybrid MSS/MSM, etc.) can be created with some difficulty, based on universal constructor technology; see Pianola breeder.
The original breeder was of type MSM (a p64 puffer puffing p30 glider guns). The known breeder with the smallest initial population is switch-engine ping-pong.
A term used in naming certain still lifes (and the stator part of certain oscillators). It indicates that the object consists of two smaller objects joined edge to edge, as in snake bridge snake.
A pattern constructed by Dean Hickerson in May 2005 which produces complex broken lines of gliders and blocks.
= soup
A Spartan elementary conduit discovered by Michael Simkin on 25 April 2016, one of the relatively few known conduits that can move a B-heptomino input to a B-heptomino output without an intervening Herschel stage.
A track for B-heptominoes. A B-heptomino becomes a Herschel plus a block in twenty generations, so this term was nearly synonymous with Herschel track until the discovery of elementary conduits that convert a B directly to another B, or to some other non-Herschel signal output. See for example BRx46B.
A 19-cell still life made up of a bookend, a table, and a snake. Starting in 2015, with the help of Mike Playle's Bellman search program, Tanner Jacobi discovered a surprising number of ways to use this object as a catalyst for signal circuitry. One example can be seen in the CC semi-cenark entry.
A queen bee shuttle stabilized at one end by an eater in such a way that it can turn a glider, as shown below. The glider turning reaction uses a banana spark and is colour-preserving. The mechanism was found by Dave Buckingham in the 1970s. The name is due to Bill Gosper.
Generation 1 of the T-tetromino.
One of several periodic colour-preserving glider reflectors discovered by Tanner Jacobi on 6 April 2016. See p3 bumper, p4 bumper, p5 bumper, p6 bumper, p7 bumper, p8 bumper, p9 bumper, p11 bumper, and p15 bumper.
The following induction coil. By itself this is a common predecessor of the honey farm. See also cis-mirrored R-bee.
This is a parent of rabbits and was found independently by Robert Wainwright and Andrew Trevorrow.
= loaf
Found by Dave Buckingham in 1972. See also airforce.
A reaction which travels indefinitely as a wave through the components of a wick or an agar. A burning wick is known as a fuse.
If the object being burned has a spatial periodicity, then the active area of the burning usually remains bounded and so eventually develops a periodicity too. It is unknown whether this will always occur.
The speed of burning can range from arbitrarily slow up to the speed of light. The results of burning can be clean (leaving no debris), or leaving debris usually much different from the original object. In rare cases, a reburnable fuse produces an exact copy of the original object, allowing the creation of objects such as the telegraph.
In many useful cases burning can be initiated by impacting an object with gliders or other spaceships. An object might be able to burn in more than one way, depending on how the burn is initiated.
That part of the stator of an oscillator which is adjacent to the rotor. Compare casing.
The following pattern, or the formation of two beehives that it evolves into after 33 generations. (Compare teardrop, where the beehives are five cells closer together.)
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in November 1998. After 125 ticks, it produces an inverted Herschel rotated 180 degrees at (-9, -17) relative to the input. Its recovery time is 166 ticks. A ghost Herschel in the pattern below marks the output location:
A composite conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in October 1998. It is made up of three elementary conduits, HF95P + PB68B + BFx59H. After 222 ticks, it produces a mirror-reflected Herschel rotated 180 degrees, at (6, -16) relative to the input. Its recovery time is 271 ticks. A ghost Herschel in the pattern below marks the output location:
Found by Robert Wainwright.
A spaceship travelling at one tenth of the speed of light. The first such spaceship to be discovered was the orthogonally travelling copperhead, found by 'zdr' on 5 March 2016. Simon Ekström found the related fireship two weeks later. A Caterloopillar can theoretically be configured to move at c/10, but there are technical difficulties with speeds of the form 4n+2, and as of June 2018 this has not been done in practice.
A spaceship travelling at one twelfth of the speed of light. The only diagonal spaceships that are currently known to move at this speed are the Corderships. An orthogonal Caterloopillar has been configured to move at c/12.
A spaceship travelling at half the speed of light. Such spaceships necessarily move orthogonally. The first to be discovered was the LWSS. For other examples see Coe ship, ecologist, flotilla, hammerhead, hivenudger, HWSS, MWSS, puffer train, puff suppressor, pushalong, Schick engine, sidecar, still life tagalong and x66.
A spaceship travelling at one third of the speed of light. All known c/3 spaceships travel orthogonally. The first was 25P3H1V0.1, found in August 1989 by Dean Hickerson. For further examples see brain, dart, edge-repair spaceship, fly, turtle and wasp.
A spaceship travelling at one quarter of the speed of light. The first such spaceship to be discovered was, of course, the glider, and this remained the only known example until December 1989, when Dean Hickerson found the first orthogonal example, 119P4H1V0, and also a new diagonal example (the big glider). For other examples see B29, Canada goose, crane, Enterprise, edge-repair spaceship (third pattern), non-monotonic, Orion, quarter, sparky, swan and tagalong. It is known that c/4 is the fastest possible speed for a (45-degree) diagonal spaceship.
A spaceship travelling at one fifth of the speed of light. The first such spaceship to be discovered was the snail, found by Tim Coe in January 1996. The first diagonally moving example, 295P5H1V1, was found by Jason Summers in November 2000. For other c/5 ships see 58P5H1V1, 67P5H1V1, 86P5H1V1 and spider. A Caterloopillar has also been configured to move at c/5.
A spaceship travelling at one sixth of the speed of light. The first such spaceship to be discovered was the dragon, found by Paul Tooke in April 2000. The first diagonally moving example was the seal, found by Nicolay Beluchenko in September 2005. Another orthogonal c/6 spaceship, found by Paul Tooke in March 2006, is shown below. For the smallest known c/6 spaceship see 56P6H1V0.
A spaceship travelling at one seventh of the speed of light. The first such spaceship to be discovered was the diagonally travelling lobster, found by Matthias Merzenich in August 2011. The first known orthogonal c/7 spaceship was the loafer, discovered by Josh Ball in February 2013. A Caterloopillar has been configured to move at c/7.
for some constant c, and which contains a glider (or other spaceship) bouncing between a slower receding spaceship and a fixed reflector which emits a spaceship (in addition to the reflected one) whenever the bouncing spaceship hits it.
As the receding spaceship gets further away the bouncing spaceship takes longer to complete each cycle, and so the extra spaceships emitted by the reflector are produced at increasingly large intervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the receding spaceship, then each interval is (v+u)/(v-u) times as long as the previous one. The population at time t is therefore n.log(t)/log((v+u)/(v-u)) + O(1), where n is the population of one of the extra spaceships (assumed constant).
The first caber tosser was built by Dean Hickerson in May 1991.
A stable glider reflector and glider-to-Herschel converter discovered by Paul Callahan in November 1998. Its recovery time is 575 ticks. The initial stage converts two gliders into a Herschel. A ghost Herschel in the pattern below marks the output location:
The glider from the southeast can be supplied by an Fx77 + L112 + Fx77 Herschel track, or by reflecting the output Herschel's FNG as in the p8 G-to-H. See also Silver reflector, Silver G-to-H.
= pulsar (The numbers refer to the populations of the three phases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.)
Found by Jason Summers, January 1999. It consists of a glider plus a tagalong.
By Charles Trawick. See also the note under cap.
Found by Robert Wainwright in November 1984.
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The following induction coil. It can also easily be stabilized to form a p3 oscillator. See candelabra for a slight variation on this.
Found by Robert Wainwright in September 1984 (using MW emulators at the end, instead of the monograms shown here).
That part of the stator of an oscillator which is not adjacent to the rotor. Compare bushing.
A 58-cell quadratic growth pattern found by Nick Gotts in April 2000. This was formerly the smallest such pattern known, but has since been superseded by the related metacatacryst. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
The catacryst consists of three arks plus a glider-producing switch engine. It produces a block-laying switch engine every 47616 generations. Each block-laying switch engine has only a finite life, but the length of this life increases linearly with each new switch engine, so that the pattern overall grows quadratically, as an unusual type of MMS breeder.
An online database of objects in Conway's Game of Life and similar cellular automata, set up by Adam P. Goucher in 2015 at http://catagolue.appspot.com. It gathers data from a distributed search of random initial configurations and records the eventual decay products. Within a year of operation it had completed a census of the ash objects from over two trillion asymmetric 16×16 soups. As of June 2018, well over two hundred trillion ash objects have been counted, from over a trillion asymmetric soups.
It is often possible to use Catagolue search results find equivalent glider synthesis recipes for selected parts of long-running active reactions. These random soup searches have made it possible to find efficient construction methods for thousands of increasingly rare still lifes and oscillators, and the occasional puffer or spaceship. In many of these cases a glider synthesis was previously very difficult or unknown.
An object that participates in a reaction but emerges from it unharmed. All eaters are catalysts. Some small still lifes can act as catalysts in some situations, such as the block, ship, and tub. The still lifes and oscillators that form a conduit are examples of catalysts.
A relatively rare form of catalysis occurs in a transparent debris effect, where the catalyst in question is completely destroyed and then rebuilt. The term is also sometimes used for a modification of an active reaction in a rake by passing spaceships.
A technology used (e.g., in the Caterpillar) to adjust the timing of a glider by turning it into a stationary object using one interaction, and then later restoring it using a second interaction. The interactions are caused by passing objects which are not otherwise affected. The direction of the glider is not usually changed.
Here is an example where a glider is turned into a boat by the first LWSS, and is then restored by the remaining spaceships:
Found by Dean Hickerson, August 1989. Compare with jam. In terms of its minimum population of 12 this is the smallest p3 oscillator. See also double caterer and triple caterer.
A family of adjustable-speed spaceships constructed by Michael Simkin in 2016, based on an "engineless caterpillar" idea originally proposed by David Bell. The front and back halves of Caterloopillars each function as universal constructors, with each half constructing the building blocks of the other half, while also reading and moving a construction tape. The overall design is reminiscent of M.C. Escher's lithograph "Drawing Hands". The name "Caterloopillar" is a reference to Douglas Hofstader's Strange Loop concept.
Simkin has written an automated script that can construct a Caterloopillar for any rational speed strictly less than c/4, with some exceptions. Speeds closer to the c/4 limit in general require larger constructions, and for any given computer system it is easy to choose a speed that makes it impractical to construct a Caterloopillar.
As of June 2018 one significant remaining exception is that Caterloopillars with periods c/(6+4N) can't be constructed. This is only a limitation of the current construction script, not of the underlying Caterloopillar toolkit. For technical reasons, the lowest speed that the current script can produce is around c/95. The slowest Caterloopillars that have been explicitly constructed to date are c/87 and c/92. These are among the smallest in terms of population, though their bounding boxes are larger than some of the higher-speed Caterloopillars.
A spaceship that works by laying tracks at its front end. The first example constructed was a p270 17c/45 spaceship built by Gabriel Nivasch in December 2004, based on work by himself, Jason Summers and David Bell. This Caterpillar has a population of about 12 million in each generation and was put together by a computer program that Nivasch wrote. At the time it was by far the largest and most complex Life object ever constructed, and it is still one of the largest in terms of population.
The 17c/45 Caterpillar is based on the following reaction between a pi-heptomino and a blinker:
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A different Caterpillar may be possible based on the following reaction, in which the pattern at top left reappears after 31 generations displaced by (13,1), having produced a new NW-travelling glider. In this case the tracks would be waves of backward-moving gliders.
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An optimized search program written by Michael Simkin in 2015, using brute-force enumeration of small Spartan objects in a limited area, instead of a depth-first tree search. One major purpose of CatForce is to find glider-constructible completions for signal conduits. An early CatForce discovery was the B60 conduit, which enabled a record-breaking new glider gun.
= pinwheel
Found in 1971 independently by Don Woods and Robert Wainwright. Compare with Hertz oscillator.
The colour-changing version of Tanner Jacobi's century-based semi-Snark mechanism, using a C-to-G consisting of a BTS catalyst and a block. See CP semi-cenark for the colour-preserving version, or semi-cenark for repeat time details and an alternate initial catalyst.
A small 90-degree colour-changing glider reflector requiring two input gliders on the same lane for each output glider. It was discovered by Sergei Petrov on 1 July 2013, using a custom-written search utility. It functions as a very compact period doubler in some signal circuitry, for example the linear propagator. The semi-Snark can period-double a regular glider stream of period 51 or more, or an intermittent stream with two gliders every 67 ticks or more, since the block reset glider can be sent just 16 ticks before its partner.
The fundamental unit of space in the Life universe. The term is often used to mean a live cell - the sense is usually clear from the context.
A certain class of mathematical objects of which Life is an example. A cellular automaton consists of a number of things. First there is a positive integer n which is the dimension of the cellular automaton. Then there is a finite set of states S, with at least two members. A state for the whole cellular automaton is obtained by assigning an element of S to each point of the n-dimensional lattice Zn (where Z is the set of all integers). The points of Zn are usually called cells. The cellular automaton also has the concept of a neighbourhood. The neighbourhood N of the origin is some finite (nonempty) subset of Zn. The neighbourhood of any other cell is obtained in the obvious way by translating that of the origin. Finally there is a transition rule, which is a function from SN to S (that is to say, for each possible state of the neighbourhood the transition rule specifies some cell state). The state of the cellular automaton evolves in discrete time, with the state of each cell at time t+1 being determined by the state of its neighbourhood at time t, in accordance with the transition rule.
There are some variations on the above definition. It is common to require that there be a quiescent state, that is, a state such that if the whole universe is in that state at generation 0 then it will remain so in generation 1. (In Life the OFF state is quiescent, but the ON state is not.) Other variations allow spaces other than Zn, neighbourhoods that vary over space and/or time, probabilistic or other non-deterministic transition rules, etc.
It is common for the neighbourhood of a cell to be the 3×...×3 (hyper)cube centred on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a proper subset of this cube.) This is known as the Moore neighbourhood.
A count of the number of different individual Life objects within one larger object, most often the final ash of a random soup experiment. This includes the number of blocks, blinkers, gliders, and other common objects, as well as any rarer larger still lifes, oscillators or spaceships.
Found by Bill Gosper. This combines the mechanisms of the p46 and p54 shuttles (see twin bees shuttle and p54 shuttle).
The smallest known 31c/240 spaceship, constructed by Chris Cain in September 2014 as a refinement of the shield bug.
This is a common pattern which evolves into three blocks and a blinker. In June 1996 Dave Buckingham built a neat p246 gun using a century as the engine. See also bookend and diuresis.
A 20-cell still life that functions as an eater for the active reaction produced by any century relative. The most well-known use is to replace a four-object constellation in Paul Callahan's bistable switch, as shown below. In September 2014 Josh Ball showed that a variant of this still life has a relatively inexpensive slow glider construction recipe.
Any signal circuit that accepts a century as input and produces a clean output glider. For example, in November 2017 Adam P. Goucher noticed that this previously known C-to-G converter can replace the century eater in Paul Callahan's bistable switch, producing an extra glider output.
A lane or signal path used in construction circuitry. Until the invention of single-channel construction arms, signals in a channel would usually be synchronized with one or more coordinated signals on other paths, as in the Gemini, which used twelve channels to run three construction arms simultaneously, or the 10hd Demonoid which needed only two channels. See also Geminoid.
An object whose fate is unknown, except that it appears to grow forever in an unpredictable manner. In Life, no pattern has yet been found that is chaotic. This is in contrast to many other Life-like rules, where even small objects can appear to grow chaotically.
It is possible that chaotic growth may occur rarely or even regularly for large enough random Life objects, but if so the minimum size of such patterns must be larger than what can currently be experimentally simulated (but see novelty generator).
In any case, it is not decidable whether a pattern that apparently grows randomly forever is in fact displaying chaotic growth. Continuing to evolve such a pattern might at any time result in it suddenly cleaning itself up and becoming predictable.
Name given by Conway to the following heptomino, a less common variant of the B-heptomino.
A block predecessor by C. R. Tompkins that unaccountably appeared both in Scientific American and in Winning Ways. See also grin.
A type of stable agar of density 1/2. The simplest version is formed from the tile:
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A term borrowed from chemistry to describe asymmetrical patterns with two distinct mirror-image orientations. One common use is in relation to Herschel transmitters, where the spacing between the two gliders in the tandem glider output can limit the receiver to a single chirality.
= mango
Any combination of conduits or converters that moves or processes an active signal. This includes components with multiple states such as period multipliers or switches, which can be used to build guns, logic gates, universal constructors, and other computation or construction circuitry.
See also pulsar quadrant.
= canoe
Opposite of dirty. A reaction which produces a small number of different products which are desired or which are easily deleted is said to be clean. For example, a puffer which produces just one object per period is clean. Clean reactions are useful because they can be used as building blocks in larger constructions.
When a fuse is said to be clean, or to burn cleanly, this usually means that no debris at all is left behind.
In signal circuitry, the distance from an edge shooter output lane to the last unobstructed lane adjacent to the edge-shooter circuitry. For example, an Fx119 inserter has an unusually high 27hd clearance.
Also, oscillator and eater variants may be said to have better clearance if they allow gliders or other signals to pass closer to them than the standard variant allows. The following high-clearance eater1 variant by Karel Suhajda allows gliders to pass one lane closer on the southeast side, than is allowed by the standard fishhook shape.
Found by Simon Norton, May 1970. This is the fifth or sixth most common oscillator, being about as frequent as the pentadecathlon, but much less frequent than the blinker, toad, beacon or pulsar. It is surprisingly rare considering its small size.
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The protruding cells at the edges can perturb some reactions by inhibiting the birth of a cell in a 3-cell corner. For example, a clock can be used to suppress the surplus blinker produced by an F171 conduit, significantly improving the recovery time of the circuit:
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Compare with pinwheel.
A uniquely effective method of adding a glider to the front edge of a salvo, by first constructing a clock, then converting it to a glider using a one-bit spark. Here it rebuilds a sabotaged glider in a deep pocket between other gliders:
In 2015 Chris Cain used this reaction to demonstrate conclusively that any unidirectional glider salvo, no matter how large or tightly packed, can be constructed by collisions between gliders that are initially separated by any finite distance. As a corollary, because all glider syntheses are made up of two to four unidirectional salvos, any glider-constructible object has a synthesis that starts with every glider at least N cells away from every other glider (for any chosen N).
= smoke
This name was given by Robert Wainwright to his p2 oscillator washing machine. But Achim Flammenkamp also gave this name to Achim's p4.
Any pattern in which each live cell is connected to every other live cell by a path that does not pass through two consecutive dead cells. This sense is due to Nick Gotts, but the term has also been used in other senses, often imprecise.
Conweh, creator of the Life universe.
A puffer engine discovered by Tim Coe in October 1995.
In December 2015, the Coe ship was discovered in an asymmetric random soup on Catagolue. This was the first time any non-p4 ship was discovered in a random asymmetric soup experiment, winning Adam P. Goucher a 50-euro prize offered by Ivan Fomichev.
Found by Tim Coe in August 1997.
An unknown fate pattern constructed by David Bell in December 2017 that simulates the Collatz 5N+1 algorithm using sliding block memory and p1 technology, while always having a population below 32000.
The algorithm is simple. Starting with a number, if it is even divide it by 2, otherwise multiply it by 5 and add 1. When this process is iterated a sequence of numbers is generated. When starting with the value of 7, it is currently unknown whether or not the sequence ever forms a cycle.
Because of this the fate of the simulator is also currently unknown. It may become stable, or become an oscillator with a high period, or have a bounding box which grows irregularly.
See colour of a glider. The reflector shown in p8 bouncer is colour-changing, as are its 5/6/7/8 and higher-period versions.
A cellular automaton that is the same as Life except for the use of a number of different ON states ("colours"). All ON states behave the same for the purpose of applying the Life rule, but additional rules are used to specify the colour of the resulting ON cells. Examples are Immigration and QuadLife.
The colour of a glider is a property of the glider that remains constant while the glider is moving along a straight path, but that can be changed when the glider bounces off a reflector. It is an important consideration when building something using reflectors.
The colour of a glider can be defined as follows. First choose some cell to be the origin. This cell is then considered to be white, and all other cells to be black or white in a checkerboard pattern. (So the cell with coordinates (m,n) is white if m+n is even, and black otherwise.) Then the colour of a glider is the colour of its leading cell when it is in a phase that can be rotated to look like this:
A reflector that does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. But a 90-degree reflector that does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required.
Small periodic colour-changing glider reflectors (bouncers) are known, and also small periodic colour-preserving glider reflectors (bumpers). Among stable patterns, only a small colour-preserving reflector (Snark) is known. The smallest known 90-degree colour-changing reflector is given at the end of the reflector entry.
See colour of a glider. Snarks and bumpers are colour-preserving reflectors.
A partial glider synthesis that can be used in the same way in multiple glider recipes. A component transforms part of an object under construction in a well-defined way, without affecting the rest of the object. For example, this well-known component can be used to add a hook to any object that includes a protruding table end, converting it to a long bookend:
"Component" is also used to specify any piece of an object - spaceship, oscillator, etc. - that can be combined with other components in specific ways according to a grammar to produce a variety of objects. The components can either be independent objects that only occasionally react with each other, or else they can be fused together to support each other. For example, any branching spaceship is made up of several components, and there is a single repeating component in any wicktrailer.
See composite conduit.
A signal-processing conduit that can be subdivided into two or more elementary conduits.
See universal computer.
Any arrangement of still lifes and/or oscillators that moves an active object to another location, perhaps also transforming it into a different active object at the same time, but without leaving any permanent debris (except perhaps gliders, or other spaceships) and without any of the still lifes or oscillators being permanently damaged. Probably the most important conduit is the following remarkable one (Dave Buckingham, July 1996) in which a B-heptomino is transformed into a Herschel in 59 generations.
= BFx59H.
Found by Dave Buckingham before 1973.
A general term for a group of two or more separate objects, usually small still lifes and low-period oscillators. Compare pseudo still life.
An adjustable mechanism in a universal constructor that allows new objects to be constructed in any chosen location that the arm can reach. A construction arm generally consists of a shoulder containing fixed guns or edge shooters, a movable construction elbow that slides forward and backward along the construction lane(s), and in the case of single-arm universal constructors, a hand target object at the construction site that can be progressively modified by a slow salvo to produce each desired object.
One of the components of a construction arm in a universal constructor. The elbow usually consists of a single Spartan still life or small constellation. It accepts elbow operation recipes, in the form of salvos coming from the construction arm's shoulder.
These recipes may do one of several things: 1) pull the elbow closer to the shoulder, 2) push the elbow farther from the shoulder, 3) emit a glider on a particular output lane (while also optionally pushing or pulling the elbow); 4) create a "hand" target block or other useful object as a target for output gliders, to one side of the construction lane; 5) duplicate the elbow, or 6) destroy the elbow.
Elbows that receive and emit orthogonally-travelling spaceships instead of gliders are technically possible, but no working examples are currently known. The discussion below assumes that gliders are used to communicate between the shoulder, elbow, and hand locations.
If a mechanism can be programmed to generate recipes for at least the first three options listed above, it is generally capable of functioning as a universal constructor. The main requirement is that push and pull elbow operations should be available that are either minimal (1fd) or the distances should be relatively prime.
Depending on the elbow operation library, there may be only one type of elbow, or there may be two or more elbow objects, with recipes that convert between them. The 9hd library had just one elbow type, a block. The original 10hd library had two elbows, blocks in mirror-symmetric locations; this was expanded to a larger list for the 10hd Demonoid. The 0hd Demonoid also has a multi-elbow recipe library. A slow elbow toolkit may make use of an even larger number of glider output recipes, because the target elbow object in that case is not restricted to a single diagonal line.
If only one colour, parity, or phase of glider can be emitted, then the mechanism will be limited to producing monochromatic salvos or monoparity salvos. These are less efficient at most construction tasks, but are still generally accepted to enable universal toolkits. See also half-baked knightship.
The region affected by an active reaction, such as a glider synthesis of an object. The envelope corresponds to the state-2 blue cells in LifeHistory. See also edgy.
Part of a construction arm between the shoulder and the elbow - in particular, one of the fixed lanes that elbow operation signals travel on. All known universal constructors have used arms with two or more construction lanes, except for the ones in the 0hd Demonoid and in recent single-channel construction recipes.
One or more streams of gliders or other signals fed into a universal constructor to create a target object. Compare glider recipe.
A conduit in which the input object is not of the same type as the output object. This term tends to be preferred when either the input object or the output object is a spaceship.
The following diagram shows a p8 pi-heptomino-to-HWSS converter. This was originally found by Dave Buckingham in a larger form (using a figure-8 instead of the boat). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of periods 44, 46 and 60 that can be used instead of the Kok's galaxy.
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For another periodic converter, see the glider-to-LWSS example in queen bee shuttle pair. However, many converters are stable. Examples of elementary conduit converters include BFx59H, 135-degree MWSS-to-G, and 45-degree MWSS-to-G.
The earliest and simplest stable converters known are shown below. These are an HWSS-to-loaf, MWSS-to-beehive, and LWSS-to-blinker. These can serve as memory cells, or as the first steps in constructing objects using salvos.
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A collection of spaceships all moving in the same direction at the same speed. Convoys are usually not destroyed by the reactions that they cause. Compare salvo. For examples, see reanimation, fly-by deletion and glider turner.
The following small c/10 spaceship, discovered by conwaylife.com forum user 'zdr' on 5 March 2016, using a simple depth-first search program. A glider synthesis was found on the same day.
Prefix used for things involving switch engines, after Charles Corderman.
A gun firing Corderships. The first was built by Jason Summers in July 1999, using a glider synthesis by Stephen Silver.
Any spaceship based on switch engines. These necessarily move at a speed of c/12 diagonally with a period of 96 or a multiple thereof. The first Cordership was constructed by Dean Hickerson in April 1991, using 13 switch engines. He soon reduced this to 10, and in August 1993 to 7. In July 1998 he reduced it to 6. In January 2004, Paul Tooke found the 3-engine glide symmetric Cordership shown below.
At the end of 2017, Aidan F. Pierce discovered a clean 2-engine Cordership. There is also an adjustable-length 4-engine Cordership found by Michael Simkin, made up of two identical or mirror-image 2-engine components. The leading pair of switch engines builds a block trail, which are then deleted by the trailing pair.
Corderships generate sparks which can perturb other objects in many ways, especially gliders which can reach them from the side or from behind. Some perturbations reflect gliders back the way they came, and can be used for constructions such as the caber tosser and the infinite glider hotel.
This contains two copies of the stillater rotor.
The following induction coil. See scrubber for an example of its use.
= cap
= pulsar
A colour-preserving variant of Tanner Jacobi's century-based semi-Snark mechanism, the semi-cenark. See CC semi-cenark for the colour-changing version, or semi-cenark for repeat time details and an alternate initial catalyst.
A period-multiplying colour-preserving signal conduit found by Tanner Jacobi in October 2017, producing one output glider for every two input gliders. It is made by replacing one of the eaters in a Snark with a catalyst found using Bellman. The catalyst causes the formation of a tub which requires a second glider to delete. However, this adds 5 ticks to the repeat time, so that it becomes 48. This is still 3 ticks faster than the CC semi-Snark.
= quarter.
The following spaceship found by Nicolay Beluchenko in September 2005, a minor modification of a tubeater found earlier by Hartmut Holzwart. The wing is of the same form as in the swan and Canada goose.
Found by Robert Wainwright in October 1989. The members of this family are all polyominoes.
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Found by Dave Buckingham in January 1973.
The p12 part of the following p12 oscillator, where it is hassled by a caterer, a jam and a HW emulator. This oscillator was found by Noam Elkies in January 1995.
= cauldron
A regular growth that is sometimes formed when a stream of gliders, or other spaceships, is fired into some junk.
The most common example is initiated by the following collision of a glider with a block. With a glider stream of even period at least 82, this gives a crystal which forms a pair of beehives for every 11 gliders which hit it.
Found by Rich Schroeppel, October 1970. This is one of only three essentially different p3 oscillators with only three cells in the rotor. The others are 1-2-3 and stillater.
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= loop
Found by David Bell, May 1992. A 25-glider recipe for the dart was found in December 2014 by Martin Grant and Chris Cain, making it the first glider-constructible c/3 spaceship.
Compare spark coil.
= ash.
As applied to Life, a de Bruijn graph is a graph showing which pieces can be linked to which other pieces to form a valid part of a Life pattern of a particular kind.
For example, if we are interested in still lifes, then we could consider 2×3 rectangular pieces and the de Bruijn graph would show which pairs of these can be overlapped to form 3×3 squares in which the centre cell remains unchanged in the next generation.
David Eppstein's search program gfind is based on de Bruijn graphs.
A pattern by Jared James Prince, based on David Bell's unit Life cell, in which each unit cell simulates two Life cells, in such a way that a Life universe filled with Deep Cells simulates two independent Life universes running in parallel.
In fact, a Life universe filled with Deep Cells can simulate infinitely many Life universes, as follows. Let P1, P2, P3, ... be a sequence of Life patterns. Set the Deep Cells to run a simulation of P1 in parallel with a simulation of a universe filled with Deep Cells, with these simulated Deep Cells running a simulation of P2 in parallel with another simulation of a universe filled with Deep Cells, with these doubly simulated Deep Cells simulating P3 in parallel with yet another universe of Deep Cells, and so on.
Deep Cell is available from http://psychoticdeath.com/life.htm.
The first self-constructing diagonal spaceship. A 0hd Demonoid was completed by Chris Cain in December 2015, shortly after a much larger 10hd version was constructed the previous month in collaboration with Dave Greene. The 0hd spaceship fits in a bounding box about 55,000 cells square, and displaces itself by 65 cells diagonally every 438,852 generations.
The first 0hd Demonoid was fired by a gun. No spaceship gun pattern had previously been completed before the first appearance of the actual spaceship.
In June 2017 Dave Greene completed a much simpler single-channel Demonoid using a temporary lossless elbow, which displaces itself 79 cells diagonally every 1,183,842 ticks. This was an improvement in terms of design complexity, but not in terms of speed, population, or bounding box. However, all of these could be further optimized. A smaller Hashlife-friendly single-channel Demonoid design was completed in 2018.
A simple Herschel circuit consisting of three eater1s, found by Brice Due in August 2006. An input Herschel places a boat in a location accessible to an input glider. If the boat is present, a one-time turner reaction occurs and the glider is turned 90 degrees onto a new lane.
The density of a pattern is the limit of the proportion of live cells in a (2n+1)×(2n+1) square centred on a particular cell as n tends to infinity, when this limit exists. (Note that it does not make any difference what cell is chosen as the centre cell. Also note that if the pattern is finite then the density is zero.) There are other definitions of density, but this one will do here.
In 1994 Noam Elkies proved that the maximum density of a stable pattern is 1/2, which had been the conjectured value. See the paper listed in the bibliography. Marcus Moore provided a simpler proof in 1995, and in fact proves that a still life with an m × n bounding box has at most (mn+m+n)/2 cells.
But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved. The best upper bound so far obtained is 8/13 (Hartmut Holzwart, September 1992).
The maximum possible density for a phase of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see agar), but densities arbitrarily close to 1 may perhaps be possible.
A Herschel conduit in which the input Herschel interacts with catalysts in the first few ticks. The standard interaction actually starts at T=-3, before the Herschel is completely formed. Compare independent conduit. The Herschel is prevented from emitting its first natural glider. This is useful in cases where the previous conduit cannot survive a first natural glider emitted from its output Herschel.
This term is somewhat confusing, since it is actually the previous conduit that depends on the dependent conduit to suppress the problematic glider. Dependent conduits such as the F166 and Lx200 do not actually depend on anything. They can be freely connected to any other conduits that fit, as long as the output Herschel evolves from its standard great-grandparent. As of this writing, the Fx158 is the only known case where a conduit's output Herschel has an alternate great-grandparent, which is incompatible with dependent conduits' initial transparent block.
The most common type of test reaction in memory cell circuitry. Information is stored in a memory cell by placing objects in known positions, or by changing the state of a stable or periodic toggle circuit. A destructive-read test consists of sending one or more signals to the memory cell. A distinct output signal is produced for each possible state of the memory cell, which is reset to a known "zero" or "rest" state. See for example boat-bit, keeper, and demultiplexer.
To permanently store information in a destructive-read memory cell, the output signal(s) must be used, in part, to send appropriate signals back to the memory cell to restore its state to its previous value. With output looped back to input, this larger composite circuit then effectively becomes a non-destructive read memory cell.
A dedicated construction arm in the Gemini spaceship, used only for removing previously active circuitry once it is no longer needed. More generally, any circuitry in a self-constructing pattern dedicated exclusively to cleanup.
= Herschel
= tub
Found by Dave Buckingham in 1972.
Any pattern that vanishes, but only after a long time. The following example vanishes in 130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells. E.g., for 8 cells we could have a glider heading towards an arbitrarily distant blinker.
Found by Robert Wainwright in 1972.
Opposite of clean. A reaction which produces a large amount of complicated junk which is difficult to control or use is said to be dirty. Many basic puffer engines are dirty and need to be tamed by accompanying spaceships in order to produce clean output. Similarly, a dirty conduit is one that does not recover perfectly after the passage of a signal; one or more extra ash objects are left behind (or more rarely a catalyst is damaged) and additional signals must be used to clean up the circuit before it can be re-used.
Found by David Eppstein in October 1998. His original stabilization used pentadecathlons. The stabilization with complicated still lifes shown here (in two slightly different forms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (see kidney).
The following induction coil.
The 2-cell polyomino. A number of objects, such as the HWSS and pentadecathlon, produce domino sparks.
An object that is either stable or oscillates without producing any output, until it is triggered by an appropriate signal, which then produces some desired action. For example, freeze-dried objects are dormant until the arrival of a particular glider.
The following reaction, found by David Bell in 1996, in which two gliders appear to circle around each other as they are reflected 90 degrees by a twin bees shuttle. Four copies of the reaction can be used to create a p92 glider loop which repeats the do-see-do reaction forever.
Of a gun, emitting two streams of spaceships (or rakes) every period. For examples, see B-52 bomber, Simkin glider gun, and p246 gun. In most cases, the two streams are alternately emitted 1/2 period apart. It is also possible for the two streams to be emitted simultaneously, as in this double-barrelled glider gun by Bill Gosper:
A certain reaction that can be used to stabilize the twin bees shuttle (qv). This was discovered by David Bell in October 1996.
The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an R-pentomino and a LWSS. (The LWSS version was known at least as early 1994, when Paul Callahan saw it form spontaneously as a result of firing an LWSS stream at some random junk.)
Found by Dean Hickerson, October 1989. Compare caterer and triple caterer.
Found by Robert Wainwright before September 1971.
= moose antlers. This term is no longer in use.
The following induction coil, found in 2015 to be a possible active reaction for the input or output of a converter.
Short identifier for Dean Hickerson's 'drifter' search program, used at various times to find wires, eaters, higher-period billiard table configurations, and related signal-carrying and signal-processing mechanisms. See also drifter.
This spaceship, discovered by Paul Tooke in April 2000, was the first known c/6 spaceship. With 102 cells, it was the smallest known orthogonal c/6 spaceship until Hartmut Holzwart discovered 56P6H1V0 in April 2009.
= paperclip. This term is no longer in use.
= freeze-dried.
A perturbation moving within a stable pattern. Dean Hickerson has written a search program to search for drifters, with the hope of finding one which could be moved around a track. Because drifters can be very small, they could be packed more tightly than Herschels, and so allow the creation of oscillators of periods not yet attained, and possibly prove that Life is omniperiodic. Hickerson has found a number of components towards this end, but it has proved difficult to change the direction of movement of a drifter, and so far no complete track has been found. However, Hickerson has had success using the same program to find eaters with novel properties, such as sparking eaters and the ones shown in diuresis.
A diagonal two-bit spark produced by many oscillators and eater reactions. Among other uses, it can reflect gliders 90 degrees. The following pattern shows an eater5 eating gliders and producing duoplets which are then used to reflect a separate glider stream. If only one glider is present, the eater5 successfully absorbs it, so this mechanism may be considered to be a simple AND gate.
See spark. A spark by definition dies out completely after some number of ticks.
Conway's somewhat confusing term for sparse Life.
Any still life that has the ability to interact with certain patterns without suffering any permanent damage. (If it doesn't suffer even temporary damage then it may be referred to as a rock.) The eater1 is a very common eater, and the term "eater" is often used specifically for this object. Other eaters include eater2, eater3, eater4, and eater5, and many hundreds of others are known. Below is a complex eater found by Dean Hickerson in 1998 using his dr search program. It takes 25 ticks to recover after feasting on a glider:
Some common still lifes can act as eaters in some situations, such as the block, ship, and tub. In fact the block was the first known eater, being found capable of eating beehives from a queen bee.
Usually simply called an eater, and also called a fishhook.
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This eater can be constructed using a simple two-glider collision, as shown in stamp collection. It is often modified in various ways, or welded to other objects, to allow tighter packing of circuits or to allow a signal stream to pass close by. See clearance for an eater1 variant that is 1hd shorter to the southeast than the standard fishhook form. An eater1 can also be used as a 90-degree one-time turner.
Its ability to eat various objects was discovered by Bill Gosper in 1971. The fishhook eater can consume a glider, a LWSS, and a MWSS as shown below. It is not able to consume an HWSS, however. See honey bit or killer toads for that.
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This eater was found by Dave Buckingham in the 1970s. Mostly it works like the ordinary eater1 but with two slight differences that make it useful despite its size: it takes longer to recover from each bite, and it can eat objects appearing at two different positions.
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The following eater2 variant (Stephen Silver, May 1998) can be useful for obtaining smaller bounding boxes. A more compact variant with the same purpose can be seen under gliderless.
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This large symmetric eater, found by Dave Buckingham, has a very different eating action from the eater1 and eater2. The loaf can take bites out things, being flipped over in the process. The rest of the object merely flips it back again.
Another eater by Dave Buckingham, which he found in 1971, but did not recognize as an eater until 1975 or 1976. It can't eat gliders, but it can be used for various other purposes. The four NE-most centre cells regrow in a few generations after being destroyed by taking a bite out of something, such as suppressing half of a developing traffic light as it does in the p29 pentadecathlon hassler.
A compound eater that can eat gliders coming from two different directions. Also called the tub-with-tail eater (TWIT), it is often placed along the edges of glider lanes to suppress unwanted gliders in conduits. Below is the standard form, a compact form with a long hook, and an often-useful conjoined form found with Bellman. The sidesnagger is a Spartan constellation that has a similar glider-absorbing function, using a loaf. See also 7x9 eater.
With gliders from either direction, the eater5's eating reaction creates a spark that can be used to reflect other gliders. See the example pattern in duoplet, or advance any of the topmost three gliders in the above pattern by two ticks.
Found by Dave Buckingham in 1976 or earlier.
= pentoad
Found by Robert Wainwright, February 1973.
This consists of the classic puffer train with a LWSS added to suppress the debris. See also space rake.
A spaceship which has an edge that possesses no spark and yet is able to perturb things because of its ability to repair certain types of damage to itself. The most useful examples are the following two small p3 c/3 spaceships:
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A gun or signal circuit that fires its gliders (or whatever) right at the edge of the pattern, so that it can be used to fire them closely parallel to others. This is useful for constructing complex guns. Compare glider pusher, which can in fact be used for making edge shooters.
The following diagram shows a p46 edge shooter found by Paul Callahan in June 1994.
Stable edge shooters became possible with the development of Herschel circuitry. For example, NW31, BNE14T30, RNE-19T84, and the high-clearance Fx119 inserter are often used in shotguns for complex salvos. Composite edge-shooter circuits with arbitrarily high clearance can be constructed.
A spark at the side of a spaceship that can be used to perturb things as the spaceship passes by.
A spaceship that produces one or more edge sparks.
In slow salvo terminology, an edgy glider construction recipe is one that places its final product at or very near the edge of its construction envelope. Similarly, an edgy factory will place its output object in an accessible location near the edge of its reaction envelope.
= non-spark. This term is no longer in use.
Name given by Conway to the following heptomino.
Depending on context, this term may refer to a signal elbow or a construction elbow. See also elbow ladder.
Scot Ellison's name for the type of pattern he created in which one or more gliders shuttle back and forth (using the kickback reaction) deleting the output gliders from a pair of slide guns.
A recipe, usually a salvo of gliders travelling on one or more construction lanes, that collides with an elbow constellation and performs one of the standard transformations on it: push, pull, or fire for simple construction arms, along with possible construct, duplicate-elbow, or delete-elbow ops for more complicated systems. See construction elbow.
A stabilization of ants. Dean Hickerson, February 1993.
Not reducible to a combination of smaller parts. Elementary spaceships in particular are usually those found by search programs, and they can't be subdivided into smaller spaceships, tagalongs, and supporting reactions, as contrasted with engineered macro-spaceships.
A conduit with no recognizable active signal stage besides its input and output. An early example still very commonly used is Buckingham's BFx59H, which transforms a B-heptomino into an inverted Herschel in 59 ticks. The BFx59H elementary conduit is a component in many of the original universal toolkit of Herschel conduits. An extension of the same naming convention is used for elementary conduits, with the first and last letters of the name specifying the input and output signal objects. As with Herschels, an arbitrary orientation and center point is chosen for each object. "Fx" means the signal moves forward and produces a mirror-image output. See Herschel conduit for further details.
Theoretically an elementary conduit may become a composite conduit, if another conduit can be found that shares the beginning or end of the conduit in question. In practice this happens only rarely, because many of the most likely branch points have already been identified: glider (G), LWSS (L) or MWSS (M), Herschel (H), B-heptomino (B), R-pentomino (R), pi-heptomino (P), queen bee shuttle (Q), century or bookend (C), dove (D), and wing (W). A Herschel descendant might qualify, due to the elementary conduit that can be seen in the p184 gun. However, there are very few simple conduits that produce Herschel descendants without Herschels, so in practice this is not a useful branch point.
Found by Noam Elkies in 1997.
Dave Buckingham's term for a Herschel loop that does not emit gliders (and so is "flightless"). All known Herschel loops of periods 52, 57, 58, 59 and 61 are emus. See also Quetzal.
Any one of three p4 oscillators that produce sparks similar to those produced by LWSS, MWSS and HWSS. See LW emulator, MW emulator and HW emulator. Larger emulators are also possible, but they require stabilizing objects to suppress their non-sparks and so are of little use. The emulators were discovered by Robert Wainwright in June 1980.
The active portion of an object (usually a puffer or gun) which is considered to actually produce its output, and which generally permits no variation in how it works. The other parts of the object are just there to support the engine. For examples, see puffer train, Schick engine, blinker puffer, frothing puffer and line puffer.
A rake or puffer which does not contain a specific engine for its operation. Instead it depends on perturbations of gliders or other objects by passing spaceships. The period of such objects is often adjustable, and in some cases the speed as well. An early example was the creation of c/5 rakes in September 1997, using gliders circulating among a convoy of c/5 spaceships. More recently, the passing spaceships themselves are also constructed, as in the Caterloopillar.
Found by Dave Buckingham, August 1972.
Found by Dean Hickerson, March 1993.
A pre-pulsar shuttle found by Dave Buckingham in August 1980. A variant is obtained by shifting the top half two spaces to either side.
The process or result of running one or more generations of an object. For example, a row of 10 cells evolves into a pentadecathlon.
For an unstable pattern, the time to stabilization divided by the initial population. For example, the R-pentomino has an evolutionary factor of 220.6, while bunnies has an evolutionary factor of 1925.777... The term is no longer in use.
The debris or smoke left behind by a puffer, especially if the debris is dirty and takes many generations to settle. The term is not usually used for the objects created by clean puffers.
A toolkit developed by Gabriel Nivasch in 2006, enabling the construction of patterns with asymptotic population growth matching O((log log ... log(t))) for any number of nested log operations. See also quadratic filter, recursive filter.
A pattern is said to be extensible if arbitrarily large patterns of the same type can be made by repeating parts of the original pattern in a regular way. For examples, see p6 shuttle, pentoad, pufferfish spaceship, snacker, wavestretcher, wicktrailer and branching spaceship.
= long^4
= long^3
Found by Dave Buckingham, August 1976.
See traffic lights extruder. A single-channel constructor arm has also been programmed to extrude a growing wick consisting of a chain of Snarks, again working from the stationary fencepost end of the wick with no need for a wickstretcher component.
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in February 1997. After 116 ticks, it produces a Herschel at (32, 1) relative to the input. Its recovery time is 138 ticks; this can be reduced to 120 ticks by adding extra mechanisms to suppress the internal glider. It is Spartan only if the following conduit is a dependent conduit, so that the welded FNG eater can be removed. A ghost Herschel in the pattern below marks the output location:
A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in July 1996. It is made up of two elementary conduits, HFx58B + BFx59H. After 117 ticks, it produces a Herschel at (40, -6) relative to the input. Its recovery time is 63 ticks. It can be made Spartan by replacing the snake with an eater1 in one of two orientations. A ghost Herschel in the pattern below marks the output location:
A composite conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in May 1997. It is composed of two elementary conduits, HFx107B + BFx59H. The F166 and Lx200 conduits are the two original dependent conduits (several more have since been discovered). After 166 ticks, it produces a Herschel at (49, 3) relative to the input. Its recovery time is 116 ticks. A ghost Herschel in the pattern below marks the output location:
An elementary conduit, the seventeenth Herschel conduit, discovered by Brice Due in August 2006 in a search using only eaters as catalysts. This was the first new Herschel conduit discovery since 1998. After 171 ticks, it produces a Herschel at (29, -17) relative to the input. A ghost Herschel in the pattern below marks the output location:
The conduit's recovery time is 227 ticks, slower than many of the original sixteen conduits because of the delayed destruction of a temporary blinker, though the circuit itself is clearly Spartan. The recovery time can be improved to 120 ticks by adding sparkers of various periods to suppress the blinker. See clock for a period-2 example.
The central eater in the group of three to the northwest can be removed to release an additional glider output signal on a transparent lane.
Another word for gun, but not used in the case of glider guns. The term is also used for a pattern that repeatedly manufactures objects other than spaceships or rakes. In this case the new objects do not move out of the way, and therefore must be used up in some way before the next one is made. The following shows an example of a p144 gun which consists of a p144 block factory whose output is converted into gliders by a p72 oscillator.
Common patterns of four identical objects. The five commonest are traffic light (4 blinkers), honey farm (4 beehives), blockade (4 blocks), fleet (4 ships, although really 2 ship-ties) and bakery (4 loaves, although really 2 bi-loaves). Also sometimes included is four skewed blocks.
A mechanism that emits two or more objects of some type for each one that it receives. Typically the objects are gliders or Herschels; glider duplicators are a special case.
The following reaction found by Dieter Leithner in May 1994. In the absence of the incoming LWSS the gliders would simply annihilate one another, but as shown they allow the LWSS to advance 11 spaces in the course of the next 6 generations.
The illusion of super-light-speed travel is caused by an LWSS that is always created, but is then destroyed in some cases, by a signal catching up to it from behind that necessarily never travels faster than the speed of light. It is not possible to make any use of the apparent super-light-speed signal. The front end of an output LWSS can't be distinguished from the alternative dying spark output until several more ticks have passed. Not surprisingly, this extra time is enough to drop the average speed of information transmission safely below c.
Leithner named the Fast Forward Force Field in honour of his favourite science fiction writer, the physicist Robert L. Forward. See also star gate and speed booster.
The result of evolving a pattern until its final behaviour is known. This answers such questions such as whether or not the pattern remains finite, what its growth rate is, what period the final state may settle into, and what its final census is. All small Life objects seem to eventually settle down into a mix of oscillators, simple spaceships, and occasionally small puffers. See methuselah, soup, ash.
Most sufficiently large random patterns are expected to grow forever due to the production of switch engines at their boundary. Engineered Life objects - and therefore also sufficiently large and unlikely random patterns - can have more interesting behaviour, such as breeders, sawtooths, and prime calculators. Some objects have even been constructed or designed having an unknown fate.
= parent
Abbreviation for full diagonals.
= glider
Any pattern that stabilizes one end of a wick.
A pattern constructed by Jason Summers in January 2000 that exhibits infinite growth if and only if there are no Fermat primes greater than 65537. The question of whether or not it really does exhibit infinite growth is therefore equivalent to a well-known and long-standing unsolved mathematical problem. It will, however, still be growing at generation 102585827975. The pattern is based on Dean Hickerson's primer and caber tosser patterns and a p8 beehive puffer by Hartmut Holzwart.
Name given by Conway to the following heptomino.
A domino sparker found by Simon Norton in 1970.
Any oscillator used to delete some but not all of the spaceships in a stream. An example is the blocker, which can be positioned so as to delete every other glider in a stream of period 8n+4, and can also do the same for LWSS streams. Other examples are the MW emulator and T-nosed p4 (either of which can be used to delete every other LWSS in a stream of period 4n+2), the fountain (which does the same for MWSS streams) and a number of others, such as the p6 pipsquirter, the pentadecathlon and the p72 oscillator shown under factory. Another example, a p4 oscillator deleting every other HWSS in a stream of period 4n+2, is shown below. (The p4 oscillator here was found, with a slightly larger stator, by Dean Hickerson in November 1994.)
A stream of spaceships in which there are periodic gaps in the stream. This can thin out another crossing stream by deleting the spaceships in the second stream except where the gaps occur. The filter stream is not affected by the deletions so that the same stream can thin out multiple other streams. The Caterpillar uses filter streams of MWSSs in which there is a gap every 6 spaceships. Here is part of a filter stream that thins a glider stream by 2/3:
A protruding cell in an oscillator or dying spark, with the ability to modify a nearby active reaction. Like a thumb, a finger cell appears at the edge of a reaction envelope and is the only live cell in its row or column. The finger spark remains alive for two ticks before dying, whereas a thumb cell dies after one tick. Because the key cell is kept alive for an extra tick, an alternate technical term is "held (orthogonal) bit spark". A "held diagonal bit spark" is not possible in B3/S23 for obvious reasons.
An encoded signal used in combination with push and pull elbow operations in a simple construction arm. When a FIRE signal is sent, the construction-arm elbow produces an output glider, usually at 90 degrees from the construction arm. This terminology is generally used when there is only a single recipe for such a glider output, or only one recipe for each glider colour (e.g., FIRE WHITE, FIRE BLACK).
A variant of the copperhead with a trailing component that emits several large sparks, discovered by Simon Ekström on 20 March 2016. The interaction between the copperhead and the additional component is minimal enough that the extension technically fits the definition of a tagalong. However, the extension slightly modifies two of the phases of the spaceship, starting two ticks after the phase shown below, so it's also valid to classify the fireship as a distinct spaceship.
Found by Nicolay Beluchenko, September 2003.
The glider produced at T=21 during the evolution of a Herschel. This is the most common signal output from a Herschel conduit.
A generic term for LWSS, MWSS and HWSS, or, more generally, for any spaceship. In recent years *WSS is much more commonly used to refer to the small orthogonal c/2 spaceships.
= eater1
A common formation of two ship-ties.
Any p2 oscillator. However, the term is also used in two more specific (and non-equivalent) senses: (a) any p2 oscillator whose two phases are mirror images of one another, and (b) any p2 oscillator in which all rotor cells die from underpopulation. In the latter sense it contrasts with on-off. The term has also been used even more specifically for the 12-cell flip-flop shown under phoenix.
Another name for the flip-flop shown under phoenix.
Any oscillator or spaceship that forms its mirror image halfway through its period.
A spaceship composed of a number of smaller interacting spaceships. Often one or more of these is not a true spaceship and could not survive without the support of the others. The following example shows an OWSS escorted by two HWSS.
A certain c/3 tagalong found by David Bell, April 1992. Shown here attached to the back of a small spaceship (also by Bell).
A reaction performed by a passing convoy of spaceships which deletes a common stationary object without harming the convoy. Fly-by deletion is often used in the construction of puffers and spaceships to clean up unwanted debris.
For c/2 convoys this is not usually difficult since the LWSS, MWSS, and HWSS spaceships have such useful sparks. However, some objects are more difficult to delete. For example, deleting a tub appears to require an unusual p4 spaceship.
The deletion of a pond appears to require a convoy which is 89 cells in width containing a very unusual p4 spaceship which has 273 cells. There are small objects which have no known fly-by deletion reactions. However, as in the case of reanimation, hitting them with the output of rakes is an effective brute force method.
Compare snake pit. Found by Achim Flammenkamp, July 1994.
A glider which moves at least partly in the same direction as the puffer(s) or spaceship(s) under consideration.
Found by Dean Hickerson in November 1994, and named by Bill Gosper. See also filter and superfountain.
The following constellation, sometimes considered to be one of the familiar fours.
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This is the smallest asymmetric p2 oscillator. Found by Dave Buckingham, July 1977.
A term used for a glider constructible seed that can activated in some way to produce a complex object. For example, a "freeze-dried salvo" is a constellation of constructible objects which, when triggered by a single glider, produces a unidirectional glider salvo, and nothing else. Freeze-dried salvos can be useful in slow salvo constructions, especially when an active circuit has to destroy or reconstruct itself in a limited amount of time. Gradual modification by a construction arm may be too slow, or the circuit doing the construction may itself be the object that must be modified.
The concept may be applied to other types of objects. For example, one possible way to build a gun for a waterbear would be to program a construction arm to build a freeze-dried waterbear seed, and then trigger it when the construction is complete.
Found by Robert Wainwright, July 1971.
Found by Dave Buckingham, October 1972.
is a puffer (or spaceship) whose back end appears to be unstable and breaking apart, but which nonetheless survives. The exhaust festers and clings to the back of the puffer/spaceship before breaking off. The first known frothing puffers were c/2, and most were found by slightly modifying the back ends of p2 spaceships. A number of these have periods which are not a multiple of 4 (as with some line puffers). Paul Tooke has also found c/3 frothing puffers.
The following p78 c/2 frothing puffer was found by Paul Tooke in April 2001.
See frothing puffer.
= freeze-dried.
Diagonal distance measurement, abbreviated "fd", often appropriate when a construction arm elbow or similar diagonally-adjustable mechanism is present.
Found by Dean Hickerson in September 1989. In terms of its 7×8 bounding box this is the smallest p5 oscillator.
A wick burning at one end. For examples, see baker, beacon maker, blinker ship, boat maker, cow, harvester, lightspeed wire, pi ship, reverse fuse, superstring and washerwoman. Useful fuses are usually clean, but see also reburnable fuse.
A fuse can burn arbitrarily slowly, as demonstrated by the example Blockic fuse below. A signal, alternating between glider and MWSS form, travels up and down between two rows of blocks in a series of one-time turner reactions. The spacing shown here causes the fuse to burn 24 cells to the right every 240 generations, for a speed of c/10. Moving the bottom half further from the top half by any even number of cells will slow down the burning even further.
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in September 1996. After 119 ticks, it produces an inverted Herschel at (20, 14) relative to the input. Its recovery time is 231 ticks; this can be reduced somewhat by suppressing the output Herschel's glider, or by adding extra catalysts to make the reaction settle more quickly. A ghost Herschel in the pattern below marks the output location:
A Herschel-to-glider converter and edge shooter based on an Fx119 Herschel conduit:
This edge shooter has an unusually high 27hd clearance, one of the highest known for a single small component. The only known higher-clearance edge shooters are injectors making use of multiple interacting spaceships. This makes the Fx119 inserter ideal for the construction of wide convoys whose total width can fit within its clearance distance.
The component creates a large cloud of smoke behind its emitted glider which lasts for over 90 generations. In spite of this, many tightly packed convoys can be made by injecting later gliders behind others in the convoy, helped along by the insertion reaction which is able to catch up to the existing gliders. The Fx119 inserter can place a glider on the same lane as a passing glider and as close as 15 ticks behind, which is only one step away from the minimum possible following distance.
A composite conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in February 1997. It is made up of two elementary conduits, HF94B + BFx59H. After 153 ticks, it produces an inverted Herschel at (48, -4) relative to the input. Its recovery time is 69 ticks. It can be made Spartan by replacing the snake with an eater1 in one of two orientations. A ghost Herschel in the pattern below marks the output location:
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in July 1996. After 158 ticks, it produces an inverted Herschel at (27, -5) relative to the input. Its recovery time is 176 ticks. It is the only known small conduit that does not produce its output Herschel via the usual Herschel great-grandparent, so it cannot be followed by a dependent conduit. A ghost Herschel in the pattern below marks the output location:
A composite conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in October 1997. It is made up of three elementary conduits, HF95P + PF35W + WFx46H. After 176 ticks, it produces an inverted Herschel at (45, 0) relative to the input. The recovery time of the standard form shown here is 92 ticks, but see the PF35W entry for a variant discovered in November 2017 that lowers the repeat time to 73 ticks. A ghost Herschel in the pattern below marks the output location.
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in August 1996. After 77 ticks, it produces an inverted Herschel at (25, -8) relative to the input. Its recovery time is 61 ticks; this can be reduced slightly by suppressing the output Herschel's glider, as in the L112 case. A pipsquirter can replace the blinker-suppressing eater to produce an extra glider output. It is one of the simplest known Spartan conduits, and one of the few elementary conduits in the original set of sixteen.
In January 2016, Tanner Jacobi discovered a Spartan method of extracting an extra glider output (top variant below). A ghost Herschel marks the output location for each variant.
An alternate Herschel receiver discovered by Sergei Petrov on 28 December 2011, using his previous glider to 2 blocks converter. In the pattern below the Herschel output is marked by a ghost Herschel. A glider also escapes to the northwest. For an explanation of the "G4" describing the tandem glider input, see Gn.
The following oscillator found by Gabriel Nivasch in October 2002.
= Life
A blog reporting on new Life discoveries, started by Heinrich Koenig in December 2004, currently found at http://pentadecathlon.com/lifenews/.
A configuration of ON and OFF cells that can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. This example was 9 × 33. In 1974 J. Hardouin-Duparc et al. at the University of Bordeaux 1 produced a 6 × 122 example. The following shows a 12 × 12 example found by Nicolay Beluchenko in February 2006, based on a 13 × 12 one found by Achim Flammenkamp in June 2004.
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Below is a 10×10 Garden of Eden found by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels in 2013 using SAT-solver techniques. An exhaustive search of 90-degree rotationally symmetric 10×10 patterns was possible because the symmetry reduces the number of unknown cells by a factor of four.
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Steven Eker has since found several asymmetrical Gardens of Eden that are slightly smaller than this in terms of bounding box area. Patterns have also been found that have only Garden of Eden parents. For related results see grandparent.
The first self-constructing spaceship, and also the first oblique spaceship. It was made public by Andrew Wade on 18 May 2010. It was the thirteenth explicitly constructed spaceship velocity in Life, and made possible an infinite family of related velocities. The Gemini spaceship derives its name from the Latin "gemini", meaning twins, describing its two identical halves, each of which contains three Chapman-Greene construction arms. A tape of gliders continually relays between the two halves, instructing each to delete its parent and construct a daughter configuration.
See Pianola breeder.
A type of self-constructing circuitry that borrows key ideas from Andrew Wade's Gemini spaceship, but with several simplifications. The main feature common to the Gemini spaceship is the construction recipe encoding method. Information is stored directly, and much more efficiently, in the timings of moving gliders, rather than in a static tape with 1s and 0s encoded by the presence of small stationary objects.
Unlike the original Gemini, Geminoids have ambidextrous construction arms, initially using glider pairs on two lanes separated by 9hd, 10hd, or 0hd. The design was the basis for the linear propagator and the Demonoids. A more recent development is a Geminoid toolkit using a single-channel construction arm, which allows for the possibility of multiple elbows with no loss of efficiency, or the construction of temporary lossless elbows. Compare slow elbow.
Other new developments that could be considered part of the extended "Geminoid" toolkit include freeze-dried construction salvos and seeds, used when objects must be built within a short time window, and self-destruct circuits, which are used as an alternative to a destructor arm to clean up temporary objects in a similarly short window.
The fundamental unit of time. The starting pattern is generation 0.
Found by Dave Buckingham, September 1972.
A program by David Eppstein which uses de Bruijn graphs to search for new spaceships. It was with gfind that Eppstein found the weekender, and Paul Tooke later used it to find the dragon. It is available at http://www.ics.uci.edu/~eppstein/ca/gfind.c (C source code only).
Compare lifesrc.
A dying spark made by removing one cell from the Herschel heptomino. This particular spark has the advantage that, when placed in a conduit to mark the location of an input or output Herschel, it disappears cleanly without damaging adjacent catalysts, even in dependent conduits with a block only two cells away.
A glider injection gate. This is a device for injecting a glider into a glider stream. The injected glider is synthesized from one or more incoming spaceships assisted by the presence of the GIG. (This contrasts with some other glider injection reactions which do not require a GIG, as in inject.) Gliders already in the glider stream pass through the GIG without interfering with it. A GIG usually consists of a small number of oscillators.
For example, in July 1996 Dieter Leithner found the following reaction which allows the construction of a pseudo-period 14 glider stream. It uses two LWSS streams, a pentadecathlon and a volcano.
Glider injection gates are useful for building glider guns with pseudo-periods that are of the form nd, where n is a positive integer, and d is a proper divisor of some convenient base gun period (such as 30 or 46), with d > 13.
Compare scrubber and spark coil.
The smallest, most common and first discovered spaceship. This was found by Richard Guy in 1970 while Conway's group was attempting to track the evolution of the R-pentomino. The name is due in part to the fact that it is glide symmetric. (It is often stated that Conway discovered the glider, but he himself has said it was Guy. See also the cryptic reference ("some guy") in Winning Ways.)
An infinite oscillator based on the following reaction (a variant of the rephaser). The oscillator consists of copies of this reaction displaced 2n spaces from one another (for some n>6) with blocks added between the copies in order to cause the reaction to occur again halfway through the period. The period of the resulting infinite oscillator is 8n-20. (Alternatively, in a cylindrical universe of width 2n the oscillator just consists of two gliders and two blocks.)
See glider synthesis.
Any reaction in which one input glider is converted into two output gliders. This can be done by oscillators or spaceships, or by Herschel conduits or other signal circuitry such as the stable example shown under splitter. The most useful glider duplicators are those with low periods.
The following period 30 glider duplicator demonstrates a simple mechanism found by Dieter Leithner. The input glider stream comes in from the upper left, and the output glider streams leave at the upper and lower right. One of the output glider streams is inverted, so an inverting reflector is required to complete the duplicator. To produce non-parallel output, an inline inverter could be substituted for the northmost p30 glider gun.
Spaceship convoys that can duplicate gliders are very useful since they (along with glider turners) provide a means to clean up many dirty puffers by duplicating and turning output gliders so as to impact into the exhaust to clean it up.
Glider duplicators and turners are known for backward gliders using p2 c/2 spaceships, and for forward gliders using p3 c/3 spaceships. These are the most general duplicators for these speeds.
A gun that fires gliders. For examples, see Gosper glider gun, Simkin glider gun, new gun, p45 gun.
True-period glider guns are known for some low periods, and for all periods over 53 using Herschel conduit technology. See true for a list of known true-period guns. The lowest true-period gun possible is the p14 gun since that is the lowest possible period for any glider stream, but no example has yet been found.
Pseudo-period glider guns are known for every period above 13. These are made by using multiple true-period guns of some multiple of the period, and glider injection methods to fill in the gaps.
= GIG
See lane.
A gun is said to be gliderless if it does not use gliders. The purist definition would insist that a glider does not appear anywhere, even incidentally. For a long time the only known way to construct LWSS, MWSS and HWSS guns involved gliders, and it was not until April 1996 that Dieter Leithner constructed the first gliderless gun (a p46 LWSS gun).
In October 2017 Matthias Merzenich used two copies of Tanner's p46 to create a p46 MWSS gun. This is the smallest known gliderless gun, and also the smallest known MWSS gun.
Two gliders travelling in the same direction with a specific spacetime offset. In a transceiver the preferred term is tandem glider. For several years, glider pairs on lanes separated by 9 or 10 half diagonals were the standard building blocks in Geminoid construction arm recipes. In more recent 0hd and single-channel construction toolkits, all gliders share the same lane, but glider pairs and singletons are still important concepts.
An arrangement of a queen bee shuttle and a pentadecathlon that can push the path of a passing glider out by one half-diagonal space. This was found by Dieter Leithner in December 1993 and is shown below. It is useful for constructing complex guns where it may be necessary to produce a number of gliders travelling on close parallel paths. See also edge shooter.
See reflector.
In early references this is usually shown in a larger form whose generation 1 is generation 8 of the form shown here.
A Spartan logic circuit discovered by Paul Callahan in 1996. It allows a glider signal to pass through the circuit, leaving behind a beehive that can cleanly absorb a single glider from a perpendicular glider stream. Two optional glider outputs are also shown. The circuit can't be re-used until the beehive "bit" is cleared by the passage of at least one perpendicular input. A similar mechanism discovered more recently is shown in the beehive stopper entry.
Construction of an object by means of glider collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity. That is, gliders should not have had to pass through one another to achieve the initial arrangement.
Glider syntheses for all still lifes and known oscillators with at most 14 cells were found by Dave Buckingham. As of June 2018, this limit has been increased to 18 cells.
Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create corresponding guns and rakes. Many of the c/2 spaceships that are based on standard spaceships have been synthesized, mostly by Mark Niemiec. In June 1998 Stephen Silver found syntheses for some of the Corderships (although it was not until July 1999 that Jason Summers used this to build a Cordership gun). In May 2000, Noam Elkies suggested that a 2c/5 spaceship found by Tim Coe in May 1996 might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March 2003 that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in Life of a rake which fires spaceships that travel in the same direction as the rake but more slowly.
A 3-glider synthesis of a pentadecathlon is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known.
A converter discovered by Sergei Petrov on 8 October 2011, used in his later G4 receiver.
A converter discovered by Sergei Petrov that places a block at its right edge in response to a single glider input. This has a variety of uses in Herschel circuitry and other signal-processing applications.
A certain p64 c/2 orthogonal puffer that produces two rows of blocks and two backward glider waves. Ten of these were used to make the first breeder.
Any reaction in which a glider is turned onto a new path by a spaceship, oscillator, or still life constellation. In the last two cases, the glider turner is usually called a reflector if the reaction is repeatable, or a one-time turner if the reaction can only happen once.
Glider turners are easily built using standard spaceships. The following diagram shows a convoy which turns a forward glider 90 degrees, with the new glider also moving forwards.
See also glider duplicator and reflector.
Undergoing simultaneous reflection and translation. A glide symmetric spaceship is sometimes called a flipper.
An abbreviation specific to converters that produce multiple gliders. A "G" followed by any integer value means that the converter produces a tandem glider - two parallel glider outputs with lanes separated by the specified number of half diagonals.
= fox
A cross-platform open source Life program by Andrew Trevorrow and Tomas Rokicki. Unlike most Life programs it includes the ability to run patterns using the hashlife algorithm. It is available from http://golly.sourceforge.net.
The first known gun, and indeed the first known finite pattern displaying infinite growth, found by Bill Gosper in November 1970. This period 30 gun remains the smallest known gun in terms of its bounding box, though some variants of the p120 Simkin glider gun have a lower population. Gosper later constructed several other guns, such as new gun and the p144 gun shown under factory. See also p30 gun.
A 41-cell 187×39 superlinear growth pattern found by Bill Gosper in March 2006, who named it in honour of Nick Gotts, discoverer of many other low-population superlinear patterns, such as Jaws, the mosquitoes, teeth, catacryst and metacatacryst. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
Collisions within the pattern cause it to sprout its Nth switch engine at generation T = ~224n-6. The population of the pattern at time t is asymptotically proportional to t times log(t), so the growth rate is O(t ln(t)), faster than linear growth but slower than quadratic growth.
Found by Dave Buckingham in March 1978. Compare with pi portraitor and popover.
A set of rules for connecting components together to make an object such as a spaceship, oscillator or still life. For example, in August 1989 Dean Hickerson found a grammar for constructing an infinite number of short wide c/3 period 3 spaceships, using 33 different components and a table showing the ways that they can be joined together.
A traditional name for a pattern with one or more parents but no grandparent. This was a hypothetical designation until May 2016. See grandparent for details.
A pattern is said to be a grandparent of the pattern it gives rise to after two generations. For over thirty years, a well-known open problem was the question of whether any pattern existed that had a parent but no grandparent. In 1972, LifeLine Volume 6 mentioned John Conway's offer of a $50 prize for a solution to the problem, but it remained open until May 2016 when a user with the conwaylife.com forum handle 'mtve' posted an example.
Other patterns have since been found that have a grandparent but no great-grandparent, or a great-grandparent but no great-great-grandparent. Further examples in this series almost certainly exist, but as of July 2018 none have yet been found.
Found in 1971. If you look at this in the right way you will see that it cycles through the Gray codes from 0 to 3. Compare with R2D2.
= Gray counter (This form is erroneous, as Gray is surname, not a colour.)
A spaceship that contains a region with an average density of 1/2, and which is extensible in such a way that the region of average density 1/2 can be made larger than any given square region.
See also with-the-grain grey ship, against-the-grain grey ship and hybrid grey ship.
The following common parent of the block. This name relates to the infamous Cheshire cat. See also pre-block.
A pattern whose population increases by one cell every generation. The smallest known grow-by-one object is the following 44-cell pattern (David Bell's one-cell improvement of a pattern found by Nicolay Beluchenko, September 2005).
A line ship in which the line repeatedly grows and shrinks, resulting in a high-period spaceship.
An object that moves like a spaceship, except that its front part moves faster than its back part and a wick extends between the two. Put another way, a growing spaceship is a puffer whose output is burning cleanly at a slower rate than the puffer is producing it. Examples include blinker ships, pi ships, and some wavestretchers.
A converter that takes a glider as an input signal and produces a Herschel output, which can then be used by other conduits. G-to-Hs are frequently used in stable logic circuitry. Early examples include Callahan G-to-H, Silver G-to-H, and p8 G-to-H for periodic circuits. A more compact recent example is the syringe.
= elevener
Any stationary pattern that emits spaceships (or rakes) forever. For examples see double-barrelled, edge shooter, factory, gliderless, Gosper glider gun, Simkin glider gun, new gun and true.
Any of a series of glider guns of period 144+72n (for all non-negative integers n) constructed by Dave Buckingham in 1990 based on his transparent block reaction and Robert Wainwright's p72 oscillator (shown under factory).
A single straight line of cells along the axis of symmetry of a mirror-symmetric pattern. Most commonly this is an orthogonal line, and the pattern is then odd-symmetric (as opposed to even-symmetric, where the axis of symmetry follows the boundary between two rows or columns of cells).
The birth rule for Conway's Life trivially implies that if there are no live cells in the gutter of a symmetric pattern, new cells can never be born there. For examples, see 44P5H2V0, 60P5H2V0, Achim's p4, brain, c/6 spaceship, centinal, p54 shuttle, pufferfish, snail, spider, and pulsar (in two orientations).
A self-supporting macro-spaceship with adjustable period but fixed direction, based on the half-bakery reaction. This was the first spaceship based on this reaction, constructed in December 2014 by Adam P. Goucher. It moves 6 cells horizontally and 3 cells vertically every 2621440+8N ticks, depending on the relative spacing of the two halves. It is one of the slowest known knightships, and the first one that was not a Geminoid. Chris Cain optimized the design a few days later to create the Parallel HBK.
The spaceship produces gliders from near-diagonal lines of half-bakeries, which collide with each other at 180 degrees. These collisions produce monochromatic salvos that gradually build and trigger seeds, which in turn eventually construct small synchronized salvos of gliders. These re-activate the lines of half-bakeries, thus closing the cycle and moving the entire spaceship obliquely by (6,3).
= bi-loaf.
The key reaction used in the half-baked knightship and Parallel HBK, where a half-bakery is moved by (6,3) when a glider collides with it, and the glider continues on a new lane. Ivan Fomichev noticed in May 2014 that pairs of these reactions at the correct relative spacing can create 90-degree output gliders:
A natural measurement of distance between parallel glider lanes, or between elbow locations in a universal construction arm elbow operation library. If two gliders are in the same phase and exactly lined up vertically or horizontally, N cells away from each other, then the two glider lanes are considered to be N half diagonals (hd) apart. Gliders that are an integer number of full diagonals apart must be the same colour, whereas integer half diagonals allow for both glider colours. See colour of a glider, linear propagator.
= ship-tie
A pattern that acts as a spacefiller in half of the Life plane, found by Jason Summers in May 2005. It expands in three directions at c/2, producing a triangular region that grows to fill half the plane.
To hammer a LWSS, MWSS or HWSS is to smash things into the rear end of it in order to transform it into a different type of spaceship. A hammer is the object used to do the hammering. In the following example by Dieter Leithner an LWSS is hammered by two more LWSS to make it into an MWSS.
A certain front end for c/2 spaceships. The central part of the hammerhead pattern is supported between two MWSS. The picture below shows a small example of a spaceship with a hammerhead front end (the front 9 columns).
Any object used as a slow salvo target by a construction arm.
An old MIT name for lumps of muck, from the following form (2 generations on from the stairstep hexomino):
Found by Dave Buckingham in September 1978. The name is by Dean Hickerson.
Found by David Poyner, this was the first published example of a fuse. The name refers to the fact that it produces debris in the form of blocks which contain the same number of cells as the fuse has burnt up.
A Life algorithm by Bill Gosper that is designed to take advantage of the considerable amount of repetitive behaviour in many large patterns of interest. It provides a means of evolving repetitive patterns millions (or even billions or trillions) of generations further than normal Life algorithms can manage in a reasonable amount of time.
The hashlife algorithm is described by Gosper in his paper listed in the bibliography at the end of this lexicon. Roughly speaking, the idea is to store subpatterns in a hash table so that the results of their evolution do not need to be recomputed if they arise again at some other place or time in the evolution of the full pattern. This does, however, mean that complex patterns can require substantial amounts of memory.
Tomas Rokicki and Andrew Trevorrow implemented Hashlife into Golly in 2005. See also macrocell.
See hassler.
An oscillator that works by hassling (repeatedly moving or changing) some object. For some examples, see Jolson, baker's dozen, toad-flipper, toad-sucker and traffic circle. Also see p24 gun for a good use of a traffic light hassler.
Found in 1971. See also twinhat and sesquihat.
Abbreviation for half diagonal. This metric is used primarily for relative measurements of glider lanes, often in relation to self-constructing circuitry; compare Gn.
For an oscillator or spaceship, the average number of cells which change state in each generation. For example, the heat of a glider is 4, because 2 cells are born and 2 die every generation.
For a period n oscillator with an r-cell rotor the heat is at least 2r/n and no more than r(1-(n mod 2)/n). For n=2 and n=3 these bounds are equal.
= HWSS
Found by Noam Elkies, November 1997. Compare fumarole. The smaller version shown below was found soon after by Alan Hensel using a component found by Dave Buckingham in June 1977. The top ten rows can be stabilized by their mirror image (giving an inductor) and this was the original form found by Elkies.
Found by Robert Wainwright in September 1984.
A pattern which can detect the passage of a glider without affecting the glider's path or timing. The first such device was constructed by David Bell in December 1992. The term, coined by Bill Gosper, refers to the fact that Heisenberg's Uncertainty Principle fails to apply in the Life universe. See also stable pseudo-Heisenburp and natural Heisenburp.
The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way.
See Heisenburp device.
A convoy of standard spaceships used in a Caterpillar to move some piece of debris at the speed of the Caterpillar. The following diagram illustrates the idea. The leading edge of this example helix, represented by the glider at the upper right in the pattern below, moves at a speed of 65c/213, or slightly faster than c/4.
Adjustable-speed helices can produce a very wide range of spaceship speeds; see Caterloopillar.
Any 7-cell polyplet.
The barberpole of length 7.
Any 7-cell polyomino. There are 108 such objects. Those with names in common use are the B-heptomino, the Herschel and the pi-heptomino.
The following pattern which occurs at generation 20 of the B-heptomino.
The name is commonly ascribed to the Herschel heptomino's similarity to a planetary symbol. William Herschel discovered Uranus in 1781. However, in point of fact a Herschel bears no particular resemblance to either of the symbols used for Uranus, but does closely resemble the symbol for Saturn. So the appropriate name might actually be "Huygens", but "Herschel" is now universally used by tradition.
Herschels are one of the most versatile types of signal in stable circuitry. R-pentominoes and B-heptominoes naturally evolve into Herschels, and converters have also been found that change pi-heptominoes and several other signal types into Herschels, and vice versa. See elementary conduit.
A series of Herschel conduits or other components, connected by placing them so that the output Herschels from early conduits become the input Herschels for later conduits. Often the initial component is a converter accepting some other signal type as input - usually a glider, in which case a syringe is most commonly used. The Silver reflector is a well-known early Spartan Herschel circuit from before the syringe was discovered, where the initial converter is a Callahan G-to-H.
Sometimes a direct connection between two conduits is not possible due to unwanted gliders that destroy required catalysts, or wanted gliders that are not able to escape. In this case, small "spacer" conduits such as F116, F117, Fx77, R64, L112, or L156 can be inserted between the other conduits to solve the problem.
Some converter or factory conduits do not produce a Herschel as output, instead generating other useful results such as gliders, boats or MWSSes. See Herschel-to-glider, demultiplexer, and H-to-MWSS respectively for examples of these. For those conduits which do produce an unwanted Herschel, an eater such as SW-2 can be added to delete it.
If the first and last conduits of a chain connect to each other in a loop then there is no need for a syringe to generate the first Herschel, or an eater to consume the last one. The circuit becomes a self-supporting Herschel loop. A loop is also formed by a syringe connected to a Herschel-to-glider converter, with the glider reflected back to the syringe's input with glider reflectors of the appropriate colour, usually Snarks. In either case, if the loop has a surplus glider output, it becomes a gun; if no output is available it is an emu.
Any reburnable fuse reaction involving Herschels. May refer specifically to the (23,5)c/79 Herschel climber used in the waterbear, or one of several similar reactions with various velocities. See also Herschel-pair climber.
A conduit that moves a Herschel from one place to another. See also Herschel loop.
Well over a hundred simple stable Herschel conduits are currently known. As of June 2018 the number is approximately 150, depending on the precise definition of "simple" - e.g., fitting inside a 100×100 bounding box, and producing output in no more than 300 ticks. In general a Herschel conduit can be called "simple" if its active reaction does not return to a Herschel stage except at its output. Compare elementary conduit, composite conduit. A description of common usage in complex circuitry, using syringes and Snarks to make compact connections, can be found in Herschel circuit.
The original universal set consisted of sixteen stable Herschel conduits, discovered between 1995 and 1998 by Dave Buckingham (DJB) and Paul Callahan (PBC). These are shown in the following table. In this table, the number in "name/steps" is the number of ticks needed to produce an output Herschel from the input Herschel. "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above).
----------------------------------------- name/steps m dx dy discovery ----------------------------------------- R64 R 11 9 DJB, Sep 1995 Fx77 Fflip 25 -8 DJB, Aug 1996 L112 L 12 -33 DJB, Jul 1996 F116 F 32 1 PBC, Feb 1997 F117 F 40 -6 DJB, Jul 1996 Bx125 Bflip -9 -17 PBC, Nov 1998 Fx119 Fflip 20 14 DJB, Sep 1996 Fx153 Fflip 48 -4 PBC, Feb 1997 L156 L 17 -41 DJB, Aug 1996 Fx158 Fflip 27 -5 DJB, Jul 1996 F166 F 49 3 PBC, May 1997 Fx176 Fflip 45 0 PBC, Oct 1997 R190 R 24 16 DJB, Jul 1996 Lx200 Lflip 17 -40 PBC, Jun 1997 Rx202 Rflip 7 32 DJB, May 1997 Bx222 Bflip -6 -16 PBC, Oct 1998 -----------------------------------------
See also Herschel transceiver.
A common active pattern occurring at generation 22 of a Herschel's evolution:
A specific three-tick predecessor of a Herschel, commonly seen in Herschel conduit collections that contain dependent conduits. In some situations it is helpful to display the input reaction in this form instead of the standard Herschel form.
Dependent conduit inputs are catalysed by a transparent block before the Herschel's standard form can appear, and before the Herschel's first natural glider is produced. This means that these conduits will fail if an actual Herschel is placed in the "correct" input location for a dependent conduit. Refer to F166 or Lx200 to see the correct relative placement of the standard transparent block catalyst.
Almost all known Herschel conduits produce a Herschel great-grandparent near the end of their evolutionary sequence. In the original universal set of Herschel conduits, Fx158 is the only exception.
A cyclic Herschel track. Although no loop of length less than 120 generations has been constructed it is possible to make oscillators of smaller periods by putting more than one Herschel in a higher-period track. In this way oscillators, and in most cases guns, of all periods from 54 onwards can now be constructed (although the p55 case is a bit strange, shooting itself with gliders in order to stabilize itself). A mechanism for a period-52 loop was found in April 2018, but it includes a stage where the signal is carried by a triplet of gliders so it may not be considered to be a pure Herschel loop. The missing period, 53, is a difficult case simply because 53 is prime and so no small sparkers or reflectors are available.
See Simkin glider gun and p256 gun for the smallest known Herschel loops. See also emu and omniperiodic.
Any reburnable fuse reaction involving pairs of Herschels. May refer specifically to the 31c/240 Herschel-pair climber used in the Centipede, or one of several similar reactions with various velocities. See also Herschel climber.
Any circuit that converts a tandem glider into a Herschel signal. The following diagram shows a pattern found by Paul Callahan in 1996, as part of the first stable glider reflector. Used as a receiver, it converts two parallel input gliders (with path separations of 2, 5, or 6) to an R-pentomino. The signal is then converted to a Herschel by one of several known mechanisms, the first of which was found by Dave Buckingham way back in 1972. The second is elementary conduit RF48H, found by Stephen Silver in October 1997. The receiver version shown below uses Buckingham's R-to-Herschel converter, which is made up of elementary conduit RF28B followed by BFx59H.
A method of cleanly suppressing a Herschel signal with an asynchronous boat-bit, discovered by Dean Hickerson. Here a ghost Herschel marks the location of the output signal, in cases where the boat-bit is not present. Other boat-bit locations that allow for clean suppression of a Herschel are also known.
This term is also sometimes used to refer to any mechanism that cleanly suppresses a Herschel. These usually allow the Herschel's first natural glider to escape, so they are more commonly classified as converters. See SW-2.
The largest category of elementary conduit. Gliders are very common and self-supporting, so it's much easier to find these than any other type of output signal. A large collection of these H-to-G converters has been compiled, with many different output lanes and timings. These can be used to synchronize multiple signals to produce gun patterns or complex logic circuitry. See NW31T120 for an example.
A track for Herschels. An equivalent term is Herschel circuit. See also B track.
An adjustable Herschel conduit made up of a Herschel transmitter and a Herschel receiver. The intermediate stage consists of a tandem glider - two gliders on parallel lanes - so that the transmitter and receiver can be separated by any required distance. The conduit may be stable, or may contain low-period oscillators.
Any Herschel-to-two-glider converter that produces a tandem glider that can be used as input to a Herschel receiver. If the gliders are far enough apart, and if one of the gliders is used only for cleanup, then the transmitter is ambidextrous: with a small modification to the receiver, a suitably oriented mirror image of the receiver will also work.
The following diagram shows a stable Herschel transmitter found by Paul Callahan in May 1997:
Compare negentropy, and also cauldron. Found by Conway's group in 1970.
Any 6-cell polyplet.
The barberpole of length 6.
Any 6-cell polyomino. There are 35 such objects. For some examples see century, stairstep hexomino, table, toad and Z-hexomino.
A common Herschel to B-heptomino converter, used as the first stage of F117 and many other Herschel conduits. There are two variants, both shown in the pattern below.
Name given by Conway to the following heptomino. After one generation this is the same as the I-heptomino.
A variant of the telegraph constructed by Louis-François Handfield in February 2017, using periodic components to achieve a transmission rate of one bit per 192 ticks. The same ten signals are sent as in the original telegraph and the p1 telegraph, but information is encoded more efficiently in the timing of those signals. Specifically, the new transmitter sends five bits every 960 ticks by adjusting the relative timings inside each of the five mirror-image paired subunits of the composite signal in the beehive-chain lightspeed wire fuse.
See clearance.
Any mechanism that can retrieve a signal from a spaceship lane while allowing spaceships on nearby lanes to pass by unaffected. In practice the spaceship is generally a glider. The signal is removed from the lane, an output signal is generated elsewhere, and the highway robber returns to its original state. A competent highway robber does not affect gliders even on the lane adjacent to the affected glider stream, except during its recovery period.
A perfect highway robber doesn't affect later gliders even in the lane to which it is attached, even during its recovery period. Below is a near-perfect highway robber "bait" that requires three synchronized signals to rebuild (the Herschel, B-heptomino, and glider.) The glider at the top right passes by unharmed, but another glider following on the same lane 200 ticks later will be cleanly reflected to a new path, and another glider following that one will also pass by unharmed. The only imperfection is a few ticks at the very end of the reconstruction, as the beehive is being rebuilt:
= beehive
A spaceship found by Hartmut Holzwart in July 1992. (The name is due to Bill Gosper.) It consists of a pre-beehive escorted by four LWSS. In fact any LWSS can be replaced by a MWSS or an HWSS, so that there are 45 different single-hive hivenudgers.
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A block and pond constellation used in the OTCA metapixel by Brice Due in 2006, to store and retrieve a bit of data - specifically, the presence or absence of a neighbor metacell. The "0" state of the honey bit memory unit is a simple beehive, which is also the source of the name.
An input glider collides with the beehive to convert it into the honey bit constellation, which can be thought of as a value of "1" stored in the memory unit. A passing LWSS can then test for the presence of the pond. If a collision occurs, the LWSS and the honey bit constellation are mutually annihilated, leaving just the original beehive. Below is the honeybit constellation with the two reactions occurring in the opposite order - test, then reset.
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The honey bit is also an interesting eater for the HWSS as shown below. An HWSS colliding with the pond happens to create the exact same reset glider used in the above memory unit.
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A common formation of four beehives.
Another term for a bookend. It is also used for other hook-shaped things, such as occur in the eater1 and the hook with tail, for example.
For a long time this was the smallest still life without a well-established name. It is now a vital component of the smallest known HWSS gun, where it acts as a rock.
The p2 agar that results from tiling the plane with the following pattern.
The following induction coil. It is generation 3 of the pi-heptomino. See spark coil and dead spark coil.
A Spartan converter found by Tanner Jacobi in October 2015, which converts an input Herschel to a middleweight spaceship. The key discovery was a very small but slightly dirty H-to-MWSS conduit, where a Herschel is catalyzed to produce an MWSS but also leaves behind a beehive. Prefixing two R64 conduits to this produces a composite converter that successfully deletes the beehive in advance, using the input Herschel's first natural glider.
Found by Robert Wainwright, June 1971.
Found by Robert Wainwright in June 1980. See also emulator.
A heavyweight spaceship, the fourth most common spaceship. Found by Conway in 1970 by modifying a LWSS. See also MWSS.
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The HWSS possesses both a tail spark and a domino belly spark which can easily perturb other objects as it passes by. The spaceship can also perturb some objects in additional ways. For examples, see puffer and glider turner.
Dave Buckingham found that the HWSS can be synthesized using three gliders as shown below:
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A p5 domino sparker, found by Dean Hickerson in February 1995.
A grey ship containing more than one type of region of density 1/2, usually a combination of a with-the-grain grey ship and an against-the-grain grey ship.
Name given by Conway to the following heptomino. After one generation this is the same as the H-heptomino.
A form of colourised Life in which there are two types of ON cell, a newly-born cell taking the type of the majority of its three parent cells and surviving cells remaining of the same type as in the previous generation.
A Herschel conduit in which the input Herschel produces its first natural glider. Compare dependent conduit.
without touching. The tubs used in the Gray counter are examples, as are the blocks and snakes used in the Hertz oscillator and the heptomino at the bottom of the mathematician.
Any oscillator with a row of dead cells down the middle and whose two halves are mirror images of one another, both halves being required for the oscillator to work. The classic examples are the pulsar and the tumbler. If still lifes are considered as p1 oscillators then there are numerous simple examples that include this kind of central gutter, such as table on table, dead spark coil and cis-mirrored R-bee. Some spaceships, such as the brain, the snail and the spider, use the same principle.
A pattern by David Bell, named after Hilbert's "infinite hotel" scenario in which a hotel with an infinite number of rooms has room for more guests even if it is already full, simply by shuffling the old guests around.
In this pattern, two pairs of Corderships moving at c/12 are pulling apart such that there is an ever-lengthening glider track between them. Every 128 generations another glider is injected into the glider track (see LWSS-glider bounce), joining the gliders already circulating there. The number of gliders in the track therefore increases without limit.
The tricky part of this construction is that even though all the previously injected gliders are repeatedly flying through the injection point, that point is guaranteed to be empty when it is time for the next glider to be injected.
Growth of a finite pattern such that the population tends to infinity, or at least is unbounded. Sometimes the term is used for growth of something other than population (for example, length), but here we will only consider infinite population growth. The first known pattern with infinite growth in this sense was the Gosper glider gun, created in a response to a $50 prize challenge by John Conway. Martin Gardner's October 1970 article described the challenge as "Conway conjectures that no pattern can grow without limit", but Conway later explained that he had always expected that this would be disproved. The original purpose in investigating CA rules including B3/S23 was to show that a very simple two-state rule could support a universal computer and/or universal constructor. If all finite patterns could be proven to be bounded, neither of these would be possible.
An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single cluster. This produces a stabilized switch engine of the block-laying type.
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In October 2014, Michael Simkin discovered a three-glider collision that produces a glider-producing stabilized switch engine and thus produces infinite growth from the smallest possible number of gliders (since all 71 2-glider collisions have a finite limit population).
Also of interest is the following pattern (again found by Callahan), which is the only 5×5 pattern with infinite growth. This too emits a block-laying switch engine.
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Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39×1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483.
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Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see also breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as sawtooths and a caber tosser. Another pattern with superlinear but non-quadratic growth is Gotts dots.
See also Fermat prime calculator.
= monogram
A reaction in which a hole in a regular spaceship stream is filled partially or fully by adding a new spaceship of the same type without affecting the existing spaceships in the stream. Depending on the period of the stream, different mechanisms can be used. For adding a spaceship to an existing multi-lane convoy, see inserter.
For large period glider streams, simple reactions such as LWSS-LWSS bounce and LWSS-glider bounce suffice. If Herschel technology is used, a large number of edge shooters and transparent conduits are known. Simple examples include the NW31 Herschel-to-glider converter and the Fx119 inserter.
Shown below is an injector found by Dave Buckingham that can fill a hole in a p15 glider stream:
The following reaction in which a p30 gun can be used to invert the presence or absence of gliders in a p30 stream, with the output glider stream being in the same direction as the input glider stream.
A mechanism that can add another spaceship into a stream or convoy of other spaceships without affecting the existing spaceships. For examples see Fx119 inserter, tee, GIG, clock insertion and inject.
= elevener
A common formation of six blinkers.
A temporary product of a partial slow salvo, elbow operation, or glider synthesis. An intermediate target is a useful step toward a desired outcome, but will not appear in the final construction.
A stream of spaceships which is based on a periodic stream, but which can contain holes where some of the spaceships are not present. There is a base period for the intermittent stream such that if a spaceship arrives at a specific location, then it always does so at a generation which is a multiple of the base period. For example, the output from a period 30 glider gun where every third glider is deleted is an intermittent stream. A pseudo-random glider generator can produce a complicated intermittent stream with no obvious pattern.
Intermittent streams can be used to transmit signals, where holes in the stream can also convey information. For example, the stream can be processed by an inverter having the same period.
Despite the name, an intermitting glider gun (IMG) is more often an oscillator than a gun. There are two basic types. A type 1 IMG consists of two guns firing at one another in such a way that each gun is temporarily disabled on being hit by a glider from the other gun. A type 2 IMG consists of a single gun firing at a 180-degree glider reflector in such a way that returning gliders temporarily disable the gun.
Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent stream of gliders in the IMG in such a way that gliders only occasionally escape.
A device which can be used to invert the presence or absence of spaceships in an intermittent stream of spaceships. The device must be a gun whose period matches the base period of the stream, since if there are no input spaceships then the device must produce spaceships as the result of the inversion. Typically the spaceships are gliders, and the inverter is made from a glider gun. Inverters provide a way to produce a NOT logic operation on a stream.
There are several ways to produce an inverter. The simplest method is to simply hit the output of a gun with the input stream to delete its spaceships, producing an output stream that is always turned 90 degrees from the input stream. An example is the northernmost p30 gun in the glider duplicator example pattern. For one way to produce an inverted output stream which is not turned, see inline inverter.
See inverter.
The individual polyplets of which a stable pattern consists are sometimes called islands. So, for example, a boat has only one island, while an aircraft carrier has two, a honey farm has four and the standard form of the eater3 has five.
The following methuselah found by Andrzej Okrasinski in August 2004.
= Herschel
Found by Robert Wainwright, April 1984.
A pattern constructed by Dean Hickerson in May 2005 that uses puffers to produce a line of bi-blocks that weaves back and forth in a complicated way.
Found by Achim Flammenkamp in 1988, but not widely known about until its independent discovery (and naming) by Dean Hickerson in September 1989. Compare with mold. In fact this is really very like caterer. In terms of its 7×7 bounding box it ties with trice tongs as the smallest p3 oscillator.
See lifesrc.
A breeder constructed by Nick Gotts in February 1997. In the original version Jaws had an initial population of 150, which at the time was the smallest for any known pattern with superlinear growth. In November 1997 Gotts produced a 130-cell Jaws using some switch engine predecessors found by Paul Callahan. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
Jaws consists of eight pairs of switch engines which produce a new block-laying switch engine (plus masses of junk) every 10752 generations. It is therefore an MMS breeder.
John Horton Conway. Also another name for monogram.
= Herschel
Two blocks hassled by two pentadecathlons. Found by Robert Wainwright in November 1984 and named by Bill Gosper. A p9 version using snackers instead of pentadecathlons is also possible.
= ash.
The following methuselah found by Andrzej Okrasinski in May 2004.
An oscillator discovered by Karel Suhajda on December 11, 2002. It consists of a period 15 rotor supported by the domino spark of a pentadecathlon. It provides accessible sparks that can be used to perturb reactions or thin signal streams.
A type of factory circuit that always results in the presence of an object in the output location, whether or not the object was previously present. In many cases it is easy to construct examples by connecting multiple circuits to shoot down an object with a glider, then rebuild the object again later. The smallest keeper circuits accomplish the same thing more directly with a lucky preliminary spark from the active reaction, which removes the existing object (if any) just before the construction occurs. Below is a useful block keeper with a Herschel input.
See short keys, bent keys and odd keys.
The following collision of two gliders whose product is a single glider travelling in the opposite direction to one of the original gliders. This is important in the proof of the existence of a universal constructor, and in Bill Gosper's total aperiodic, as well as a number of other constructions.
A pair of toads acting together so that they can eat things. Here, for example, are some killer toads eating an HWSS. Similarly they can eat a MWSS (but not a LWSS). For another example see twirling T-tetsons II. See also candlefrobra.
As an alternative to a torus, it's possible to make a finite Life universe in the form of a Klein bottle. The simplest way to do this is to use an m × n rectangle with the top edge joined to the bottom edge (as for a torus) and the left edge twisted and joined to the right.
/n - that is, a spaceship of any speed that moves obliquely in a (2,1) direction. The first Conway's Life knightship was a variant of Andrew Wade's Gemini spaceship, constructed in May 2010. The next was an even slower knightship based on the half-bakery reaction.
A knightship must be asymmetric and its period must be at least 6. This is barely within the range of current search programs, as proven by the discovery on March 6, 2018 of an elementary knightship, Sir Robin, by Adam P. Goucher and Tomas Rokicki.
By analogy with the corresponding fairy chess pieces, spaceships of types (3m,m)/n, (3m,2m)/n and (4m,m)/n would presumably be called camelships, zebraships and giraffeships, respectively. Such spaceships do exist (see universal constructor) but small elementary versions are even more difficult to search for. Any of these ship types could be constructed by trivially modifying a Gemini spaceship, or less trivially by reprogramming one of the more recent small Geminoid construction arms, but as of July 2018 a camelship Gemini is the only example that has been explicitly built.
Alternatively, the term "knightship" is regularly used to refer to any oblique spaceship, such as the original Gemini or the waterbear.
An oscillator found by Jan Kok in 1971, currently serving as the icon for Golly. See converter for a use of this sparker.
A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in July 1996. It is made up of two elementary conduits, HLx53B + BFx59H. After 112 ticks, it produces a Herschel turned 90 degrees counterclockwise at (12, -33) relative to the input. Its recovery time is 61 ticks; this can be reduced slightly by removing the output glider, either with a specialized eater (as in the original true p59 gun), or with a sparker as in most of the Quetzal guns. It can be made Spartan by replacing the aircraft carrier with an eater1. A ghost Herschel in the pattern below marks the output location:
A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in August 1996. It is made up of three elementary conduits, HLx69R + RF28B + BFx59H. After 156 ticks, it produces a Herschel turned 90 degrees counterclockwise at (17, -41) relative to the input. Its recovery time is 62 ticks. It can be made Spartan by replacing the snake with an eater1 in one of two orientations. Additional gliders can be produced by removing the southeasternmost eater, or by replacing the RF28B elementary conduit by an alternate version. A ghost Herschel in the pattern below marks the output location:
Any still life consisting of a simple closed curve made from diagonally connected dominoes. The smallest example is the pond, and the next smallest is this (to which the term is sometimes restricted):
A path traveled by a glider, or less commonly a spaceship such as a loafer. The lane is centered on the line of symmetry (if any) of the spaceship in question. If a lane is clear, then the spaceship can travel along it without colliding or interfering with any other objects.
Diagonal lanes are often numbered consecutively, in half-diagonals (hd). Occasionally diagonal lane measurements are given in quarter-diagonals (qd), in part because diagonally symmetric spaceships have a line of symmetry 1qd away from the lines available for gliders. It's also convenient that moving a glider forward by 100qd (for example) has the same effect as evolving the same glider for 100 ticks.
Found by Rich Schroeppel, September 1992.
Any oscillator with a relatively small bounding box whose period is a very large prime. (If the bounding-box restriction is removed, then eight gliders travelling in a four-Snark loop would provide a trivial example for any chosen prime.) The first such oscillator was built by Gabriel Nivasch in 2003. The current record holder is an oscillator constructed by Adam P. Goucher with a period that is a Mersenne prime with 13,395 digits (244497-1).
The next higher Mersenne-prime oscillator, period 286243-1, could be constructed with quadri-Snarks and semi-Snarks. It would actually be significantly smaller than the current record holder. As of June 2018 the construction of this pattern has not yet been completed.
= big S
A methuselah found by Andrzej Okrasinski in July 2005.
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A 2-dimensional 2-state cellular automaton discovered by John Conway in 1970. The states are referred to as ON and OFF (or live and dead). The transition rule is as follows: a cell that is ON will remain ON in the next generation if and only if exactly 2 or 3 of the 8 adjacent cells are also ON, and a cell that is OFF will turn ON if and only if exactly 3 of the 8 adjacent cells are ON. (This is more succinctly stated as: "If 2 of your 8 nearest neighbours are ON, don't change. If 3 are ON, turn ON. Otherwise, turn OFF.")
A freeware Life program by Johan Bontes for Microsoft Windows 95/98/ME/NT/2000/XP: https://github.com/JBontes/Life32/.
A multistate CA rule supported by Golly, equivalent to two-state B3/S23 Life but with several additional states intended for annotation purposes. A "history" state records whether an off cell has ever turned on in the past, and other states allow on and off cells to be permanently or temporarily marked, without affecting the evolution of the pattern.
A shareware Life program by Andrew Trevorrow for the Macintosh (MacOS 8.6 or later): http://www.trevorrow.com/lifelab/.
A newsletter edited by Robert Wainwright from 1971 to 1973. During this period it was the main forum for discussions about Life. The newsletter was nominally quarterly, but the actual dates of its eleven issues were as follows:
Mar, Jun, Sep, Dec 1971 Sep, Oct, Nov, Dec 1972 Mar, Jun, Sep 1973
A Life enthusiast. Term coined by Robert Wainwright.
David Bell's Life search program for finding new spaceships and oscillators. This is a C implementation of an algorithm developed by Dean Hickerson in 6502 assembler.
Although lifesrc itself is a command-line program, Jason Summers has made a GUI version called WinLifeSearch for Microsoft Windows. A Java version, JavaLifeSearch, was written in November 2012 by Karel Suhajda.
The lifesrc algorithm is only useful for very small periods, as the amount of computing power required rises rapidly with increasing period. For most purposes, period 7 is the practical limit with current hardware.
Lifesrc is available from http://tip.net.au/~dbell/ (source code only). Compare gfind.
A scriptable Javascript Life pattern viewer written by Chris Rowett, used primarily on the conwaylife.com discussion forums.
Found in 1971.
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A type of negative spaceship travelling through the zebra stripes agar. The center of the bubble is simple empty space, and the length and/or width of the bubble can usually be extended to any desired size.
Below is a small stabilized section of agar containing a sample lightspeed bubble, found by Gabriel Nivasch in August 1999. The bubble travels to the left at the speed of light, so it will eventually reach the edge of any finite patch and destroy itself and its supporting agar.
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An open problem related to lightspeed bubbles was whether large extensible empty areas could be created whose length was not proportional to the width (as it must be in the above case, due to the tapering back edge). This was solved in February 2017 by Arie Paap; a simple period-2 solution is shown below.
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= telegraph.
Any wick that can burn non-destructively at the speed of light. Lightspeed wires are a type of reburnable fuse. These are potentially useful for various things, but so far the necessary mechanisms are very large and unwieldy. In October 2002, Jason Summers discovered a lightspeed reaction travelling through an orthogonal chain of beehives. Summers completed a period-1440 lightspeed telegraph based on this reaction in 2003.
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A stable lightspeed transceiver mechanism using this same signal reaction, the p1 telegraph, was constructed by Adam P. Goucher in 2010; the bounding boxes of both the transmitter and receiver are over 5000 cells on a side. A more compact periodic high-bandwidth telegraph with a much improved transmission rate was completed by Louis-François Handfield in 2017.
The following diagram shows an older example of a lightspeed wire, with a small defect that travels along it at the speed of light. As of June 2018, no method has been found of creating such a defect in the upstream end of this particular stable wire, or of non-destructively detecting the arrival of the defect and repairing the wire at the downstream end.
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= LWSS
= toaster
A growth rate proportional to T, where T is the number of ticks that a pattern has been run. Compare superlinear growth, quadratic growth.
A self-replicating pattern in which each copy of a pattern produces one child that is an exact copy of itself. The child pattern then blocks the parent from any further replication. An example was constructed by Dave Greene on 23 November 2013, with a construction arm using two glider lanes separated by 9hd. By some definitions, due to its limited one-dimensional growth pattern, the linear propagator is not a true replicator. Compare quadratic replicator.
A pattern which is able to send a signal across an infinite diagonal line of live cells without destroying the line. David Bell built one in August 2006. It uses many one-shot period 44160 glider guns on both sides of the line having the proper synchronization to create the reactions shown in line-cutting reaction and line-mending reaction.
An input glider can arrive at any multiple of 44160 generations to first cut the line, then send a glider through the gap, and finally mend the line while leaving an output glider on the other side.
A line crosser whose complete mechanism is on one side of the line is theoretically possible, using single-channel construction methods for example.
A reaction that can cut an infinite diagonal line of cells, leaving a gap with both ends sealed. Such a reaction is demonstrated below. In actual use the reaction should be spread out so that the incoming LWSSes don't conflict. See line-mending reaction for a way to mend the gap.
A reaction which can fully mend a sealed gap in an infinite diagonal line of cells, such as the one produced by a line-cutting reaction. Such a reaction is demonstrated below. See the line cutting reaction for a way of creating the gliders travelling parallel to the line.
This reaction uses spaceships on both sides of the line which need to be synchronized to each other, for example by passing a glider through the gap to trigger the creation of the required spaceships and gliders.
No simple mechanism is known to mend the gap which lies completely on one side of the line. However, it is technically possible to use construction arm technology to push objects through the gap to build and trigger a seed for the required synchronized signals on the other side.
A puffer which produces its output by means of an orthogonal line of cells at right angles to the direction of travel. The archetypal line puffer was found by Alan Hensel in March 1994, based on a spaceship found earlier that month by Hartmut Holzwart. The following month Holzwart found a way to make extensible c/2 line puffers, and Hensel found a much smaller stabilization the following day. But in October 1995 Tim Coe discovered that for large widths these were often unstable, although typically lasting millions of generations. In May 1996, however, Coe found a way to fix the instability. The resulting puffers appear to be completely stable and to exhibit an exponential increase in period as a function of width, although neither of these things has been proved.
Line puffers have enabled the construction of various difficult periods for c/2 spaceships and puffers, including occasionally periods which are not multiples of 4 and which would therefore be impossible to attain with the usual type of construction based on standard spaceships. (See frothing puffer for another method of constructing such periods.) In particular, the first c/2 rake with period not divisible by 4 was achieved in January 2000 when David Bell constructed a p42 backrake by means of line puffers.
See also hivenudger and puff suppressor.
A spaceship in which the front end is a linestretcher, the line being eaten by the back end.
A wickstretcher that stretches a single diagonal line of cells. The first example was constructed by Jason Summers in March 1999; this was c/12 and used switch engine based puffers found earlier by Dean Hickerson. The first c/4 example was found by Hartmut Holzwart in November 2004.
Found by Dave Buckingham, September 1972.
A small c/7 spaceship discovered by Josh Ball on 17 February 2013:
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It has a known 8-glider construction recipe, probably not minimal, discovered on the following day:
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Here four pentadecathlons hassle a loaf. Found by Robert Wainwright in 1990.
= bi-loaf
The following glider/loaf collision, which pulls a loaf (3,1) toward the glider source:
A spaceship discovered by Matthias Merzenich in August 2011, the first diagonally travelling c/7 spaceship to be found. It consists of two gliders pulling a tagalong that then rephases them.
A pattern whose population or bounding box grows no faster than logarithmically, asymptotic to n.log(t) for some constant n. The first such pattern constructed was the caber tosser whose population is logarithmic, but whose bounding box still grows linearly. The first pattern whose bounding box and population both grow logarithmically was constructed by Jason Summers with Gabriel Nivasch in 2003. For a pattern with a slower growth rate than this, see Osqrtlogt.
An agar in which every live cell is isolated in every generation. There are many different lone dot agars. All of them are phoenixes. In 1995 Dean Hickerson and Alan W. Hensel found stabilizations for finite patches of ten lone dot agars to create period 2 oscillators. One of these is shown below:
A term applied to an object that is of the same basic form as some standard object, but longer. For examples see long barge, long boat, long bookend, long canoe, long shillelagh, long ship and long snake.
The next degree of longness after long long. Some people prefer "extra long".
The next degree of longness after long^3. Some people prefer "extra extra long".
The following induction coil, longer than a bookend.
= loop
= dock
The next degree of longness after long. Some people prefer "very long".
A stationary elbow in a construction arm toolkit that allows a recipe to turn a corner with no exponential increase in construction cost. Compare slow elbow. It is theoretically possible to construct lossless elbows for early construction arms such as the one in the 10hd Demonoid, but these would currently have to be very large.
The lossless elbow that has been used the most in practice is the Snark, which can be constructed directly on a single-channel construction lane using a Snarkmaker recipe. Controlled demolition of a Snark is also possible, to remove a temporary elbow that is no longer needed, and leave a hand target in its place if necessary for further construction.
A Silver reflector was used as a lossless elbow in the first spiral growth pattern, attached to a separate universal constructor component.
The common evolutionary sequence that ends in the blockade. The name is sometimes used of the blockade itself, and can in general be used of any stage of the evolution of the stairstep hexomino.
emulator, found by Robert Wainwright in June 1980.
A lightweight spaceship, the smallest known orthogonally moving spaceship, and the second most common (after the glider). Found by Conway when one formed from a random soup in 1970. See also MWSS and HWSS.
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The LWSS possesses a tail spark which can easily perturb other objects which grow into its path. The spaceship can also perturb some objects in additional ways. For examples, see blinker ship, hivenudger, and puffer train.
Dave Buckingham found that the LWSS can be synthesized in several different ways using three gliders, and can be constructed from two gliders and another small object in several more ways. Here is the fastest synthesis:
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The following reaction in which a LWSS and a glider collide to form a glider heading back between the two input paths:
The following symmetric reaction in which two LWSSs collide head-on to form two gliders heading apart at 90 degrees from each other. Compare LWSS-LWSS deflection.
The following symmetric reaction in which two LWSSs collide nearly head-on to form two gliders heading apart at 180 degrees from each other. Compare LWSS-LWSS bounce.
See 135-degree MWSS-to-G.
Life Worker Time Deficiency Syndrome. Term coined by Dieter Leithner to describe the problem of having to divide scarce time between Life and real life.
= toaster
A composite conduit, one of the original sixteen Herschel conduits, discovered by Paul Callahan in June 1997. It is made up of two elementary conduits, HL141B + BFx59H. The Lx200 and F166 conduits are the two original dependent conduits (several more have since been discovered.) After 200 ticks, it produces an inverted Herschel turned 90 degrees counterclockwise at (17, -40) relative to the input. Its recovery time is 90 ticks. It can be made Spartan by replacing the snakes with eater1s in one of two orientations. A ghost Herschel in the pattern below marks the output location:
A format used by Golly and its hashlife algorithm, capable of storing repetitive patterns very efficiently, even if they contain a large number of cells. For example, a filled square 2167 cells on a side can be stored in less than three kilobytes in macrocell format, or about 800 bytes in compressed macrocell format. The square's total population is over a googol, 10100; the number of atoms in the observable universe is only about 1080.
This high level of compression is obtained by defining a tree structure composed of increasingly large cell "tiles" with power-of-two dimensions. Tile definitions of any size are re-used whenever they appear multiple times in a large pattern (at the same power-of-two offset). For example, the following is a macrocell encoding of a complex pseudo still life arrangement of ships, with a total population over 2500 cells:
[M2] (golly 3.0) #R B3/S23 .OO.OO$O.O.O.O$OO...OO$$OO...OO$O.O.O.O$.OO.OO$ 4 0 1 1 1 5 2 0 2 2 6 3 3 0 3 7 4 4 4 4
The first line after the #R rule line defines a quadtree tile at the lowest level - a level-3 tile in this case, meaning a 23 square area. At this level the pattern is encoded in a modified ASCII format with dollar signs as line separators. The next line, #2, defines a level-4 quadtree tile, made from one empty level-3 tile in the northwest corner (0), and three copies of the level-3 tile that was defined on the previous line (1). Lines 3, 4, and 5 similarly define level 5, 6, and 7 quadtree tiles by giving the line numbers of four tiles of the next lower size.
Many patterns are only moderately repetitive, so macrocell format is somewhat less successful at compressing them. Certainly most patterns are not nearly as regular as the artificial example above: there are usually many different tiles defined at each level, not just one. Chaotic patterns, such as ash from random soups, usually need so many different tile definitions that they can be stored more efficiently using rle format.
A self-constructing or self-supporting spaceship, such as the Caterpillar, Centipede, half-baked knightship, waterbear, Demonoid, Orthogonoid, and Caterloopillar. Engineered spaceships of these types tend to be much larger and more complex than elementary spaceships.
A relatively rare 180-degree rotationally symmetric 8-bit still life. The acorn produces a mango as part of its ash.
Found by Dave Buckingham, 1972.
A name for the smallest known spacefiller. The name represents the fact that the growth rate is the fastest possible. (This has not quite been proved, however. There remains the possibility, albeit not very likely, that a periodic agar could have an average density greater than 1/2, and a spacefiller stretching such an agar at the same speed as the known spacefillers would have a faster average growth rate.)
In terms of its minimum population of 12 this ties with mold as the smallest p4 oscillator. Found by Dave Buckingham in December 1973. For some constructions using mazings, see popover and sixty-nine.
= MWSS
= p1 megacell.
A type of information storage circuit useful in many patterns that perform complex logical operations. Most commonly a memory cell can store a single bit of information. See for example demultiplexer, honey bit, and boat-bit. Depending on the application, the circuit may be a toggle circuit or a permanent switch, or it may be possible to send one or more signals to set the circuit to a "1" state, as can be done with a keeper mechanism. In that case a different input signal must be used to test the current state, usually with a destructive read reaction.
A more complicated example can be found in the Osqrtlogt pattern, which destructively reads a growing 2-dimensional array of minimal memory cells. Each memory cell may either contain a boat (below left) or empty space (below right), with no permanent circuitry anywhere near:
Found by Matthias Merzenich in December 2010.
Found by Matthias Merzenich in June 2011.
A 52-cell pattern exhibiting quadratic growth. Found by Nick Gotts, December 2000. This was for some time the smallest known pattern (in terms of initial population) with superlinear growth. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
CA logic circuitry that emulates the behavior of a single cell. The circuitry is hard-wired to emulate a particular CA rule, but changing the rule is usually a matter of making simple adjustments. Known examples include David Bell's original 500×500 unit Life cell, Jared Prince's Deep Cell, Brice Due's OTCA metapixel, and Adam P. Goucher's megacell.
An oscillator built by Robert Wainwright that uses the following reaction (found by Bill Gosper) to turn gliders into LWSS, and converts these LWSS back into gliders by colliding them head on using an LWSS-LWSS bounce. There are two ways to do the following reaction, because the twin bees shuttle spark is symmetric.
An oscillator built by Robert Wainwright in December 1994 based on the following p30 glider-to-LWSS converter using a queen bee shuttle pair. This converter was first found by Paul Rendell, January 1986 or earlier, but wasn't widely known about until Paul Callahan rediscovered it in December 1994.
See metacell, OTCA metapixel.
Any small pattern that stabilizes only after a long time. Term coined by Conway. Examples include rabbits, acorn, the R-pentomino, blom, Iwona, Justyna and Lidka. See also ark.
The following still life, named by Mark Niemiec:
= MWSS
Found by Robert Wainwright before June 1972. Compare pressure cooker.
The maximum population divided by the initial population for an unstable pattern. For example, the R-pentomino has an M.I.P. value of 63.8, since its maximum population is 319. The term is no longer in use.
= cuphook
See breeder.
See breeder.
The smallest number of generations it takes for an oscillator or spaceship to reappear in its original form, possibly subject to some rotation or reflection. The mod may be equal to the period, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators which rotate 180 degrees every half period, and also for flippers).
Found by Achim Flammenkamp in 1988, but not widely known until Dean Hickerson rediscovered it (and named it) in August 1989. Compare with jam. In terms of its minimum population of 12 it ties with mazing as the smallest p4 oscillator. But in terms of its 6×6 bounding box it wins outright. In fact, of all oscillators that fit in a 6×7 box it is the only one with period greater than 2.
A slow salvo that uses gliders of only one colour. For example, the slow salvos generated by half-baked knightships are monochromatic, because they are generated by a single type of reaction which can happen at any position along a diagonal line. The smallest possible step size is one full diagonal (1fd), which is two half diagonals (2hd), which means that any single glider-producing reaction can only reach half of the available glider lanes. See colour of a glider.
Found by Dean Hickerson, August 1989.
A slow salvo that uses gliders of only one parity. Compare monochromatic salvo.
The set of all cells that are orthogonally or diagonally adjacent to a cell or group of cells. The Moore neighbourhood of a cell can be thought of as the points at a Chebyshev distance of 1 from that cell. Compare von Neumann neighbourhood. The Conway's Life rule is based on the Moore neighborhood, as are all the "Life-like" rules and many other commonly investigated rule families.
Cell neighbourhoods can also be defined with a higher range. The Moore neighbourhood of range n can be defined recursively as the Moore neighbourhood of the Moore neighbourhood of range n-1. For example, the Moore neighbourhood of range 2 includes all cells that are orthogonally or diagonally adjacent to the standard Moore neighbourhood.
See mosquito1, mosquito2. mosquito3, mosquito4 and mosquito5.
A breeder constructed by Nick Gotts in September 1998. The original version had an initial population of 103, which was then the smallest for any known pattern with superlinear growth (beating the record previously held by Jaws). This was reduced to 97 by Stephen Silver the following month, but was then almost immediately superseded by mosquito2.
Mosquito1 consists of the classic puffer train plus four LWSS and four MWSS (mostly in predecessor form, to keep the population down). Once it gets going it produces a new block-laying switch engine (plus a lot of junk) every 280 generations. It is therefore an MMS breeder, albeit a messy one.
A breeder constructed by Nick Gotts in October 1998. Its initial population of 85 was for a couple of hours the smallest for any known pattern with superlinear growth, but was then beaten by mosquito3.
Mosquito2 is very like mosquito1, but uses two fewer MWSS and one more LWSS.
A breeder constructed by Nick Gotts in October 1998. Its initial population of 75 was at the time the smallest for any known pattern with superlinear growth, but was beaten a few days later by mosquito4.
Mosquito3 has one less LWSS than mosquito2. It is somewhat different from the earlier mosquitoes in that the switch engines it makes are glider-producing rather than block-laying.
A slightly improved version of mosquito3 which Stephen Silver produced in October 1998 making use of another discovery of Nick Gotts (September 1997): an 8-cell pattern that evolves into a LWSS plus some junk. Mosquito4 is a breeder with an initial population of 73, at the time the smallest for any known pattern with superlinear growth, but superseded a few days later by mosquito5.
A slightly improved version of mosquito4 which Nick Gotts produced in October 1998. The improvement is of a similar nature to the improvement of mosquito4 over mosquito3. Mosquito5 is a breeder with an initial population of 71. This was the smallest population for any known pattern with superlinear growth until it was superseded by teeth. See switch-engine ping-pong for the smallest such pattern as of July 2018, along with a list of the record-holders.
= mold
A sawtooth such that no cell is ON for more than a finite number generations. David Bell constructed the first pattern of this type, with a c/2 front end and a c/3 back end. The front end is a blinker puffer. The back end ignites the blinker fuse.
The smallest currently known moving sawtooth was constructed in April 2011 by a conwaylife.com forum user with the handle 'cloudy197'. The c/2 front end is a bi-block puffer. The 2c/5 back end ignites the bi-block fuse.
See breeder.
An extensible oscillator family consisting of one or more roteightor rotors, discovered by Dean Hickerson in 1990.
In a reflectorless rotating oscillator, the maximum number n of independent patterns that can orbit a single point, in a way that reduces the period of the combined oscillator by a factor of n.
A methuselah found by Charles Corderman, but not as long-lasting as his acorn.
Any oscillator whose rotor consists of a closed chain of cells each of which is adjacent to exactly two other rotor cells. Compare babbling brook. Examples include the bipole, the blinker, the clock, the cuphook, the Gray counter, the quad, the scrubber, the skewed quad and the p2 snake pit. The following diagram shows a p2 example (by Dean Hickerson, May 1993) with a larger rotor. See ring of fire for a very large one.
Found by Robert Wainwright in June 1980. See also emulator and filter.
A middleweight spaceship, the third most common spaceship. Found by Conway in 1970 by modifying a LWSS. See also HWSS.
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The MWSS possesses both a tail spark and a belly spark which can easily perturb other objects as it passes by. The spaceship can also perturb some objects in additional ways. For examples see blinker puffer and glider turner.
Dave Buckingham found that the MWSS can be synthesized using three gliders, and can be constructed from two gliders and another small object in several more ways. Here is the glider synthesis:
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The following reaction, found by Peter Rott in November 1997, in which a LWSS passing by a p46 oscillator creates a MWSS travelling in the opposite direction. Together with some reactions found by Dieter Leithner, and an LWSS-turning reaction which Rott had found in November 1993 (but which was not widely known until Paul Callahan rediscovered it in June 1994) this can be used to prove that there exist gliderless guns for LWSS, MWSS and HWSS for every period that is a multiple of 46.
Found by Dean Hickerson in April 1992.
An article by Dave Buckingham (October 1996) available from http://conwaylife.com/ref/lifepage/patterns/bhept/bhept.html. It describes his discovery of Herschel conduits, including sufficient (indeed ample) stable conduits to enable, for the first time, the construction of period n oscillators and true period n guns for every sufficiently large integer n. See Herschel loop and emu.
Occurring often in random patterns. There is no precise measure of naturalness, since the most useful definition of "random" in this context is open to debate. Nonetheless, it is clear that objects such as blocks, blinkers, beehives and gliders are very natural, while eater2s, darts, guns, etc., are not.
A twin bees shuttle pair arrangement found by Brice Due in 2006. A glider passes through the reaction area of the shuttle pair completely unaffected. However, a Heisenburp effect causes a second glider to be created "out of the blue", following behind the first at a 2hd offset.
A type of signal travelling through a periodic agar such as zebra stripes. The leading edge of the signal removes the agar, and the trailing edge rebuilds the agar some time later. The distance between the two edges is sometimes adjustable, as shown in lightspeed bubble. The central part of the "spaceship" may consist of dying sparks or even simple empty space.
Below is a sample period-5 negative spaceship, found by Hartmut Holzwart in March 2007, in a small stabilized section of zebra stripes agar:
Compare Hertz oscillator.
Any of the eight cells adjacent to a given cell. A cell is therefore not considered to be a neighbour of itself, although the neighbourhood used in Life does in fact include this cell (see cellular automaton).
Found by Dean Hickerson, January 1990.
An old name for the period 46 glider gun show below. This was found by Bill Gosper in 1971, and was the second basic glider gun found (after the Gosper glider gun). It produces a period 46 glider stream.
A number of other ways of constructing a gun from two twin bees shuttles have since been found. See edge shooter for one of these, and see also p46 gun.
The following diagonal puffer consisting of two switch engines. This was found by Charles Corderman in 1971. The name comes from the variety of objects it leaves behind: blocks, blinkers, beehives, loaves, gliders, ships, boats, long boats, beacons and block on tables.
See also ark.
Any polyomino with exactly n cells.
A type of test reaction in memory cell circuitry, where the information in the memory cell is unchanged and can be read again to produce the same result. One simple type of non-destructive read reaction is a signal sent to a permanent switch. Memory cells with destructive read reactions are generally simpler and more commonly used.
A spaceship is said to be non-monotonic if its leading edge falls back in some generations. The first example (shown below) was found by Hartmut Holzwart in August 1992. This is p4 and travels at c/4. In April 1994, Holzwart found examples of p3 spaceships with this property, and this is clearly the smallest possible period. Another non-monotonic spaceship is the weekender.
This is the unique nonomino (a polyomino having 9 cells) whose evolution results in a switch engine, and the smallest polyomino to do so.
Charles Corderman may have found this object in 1971 while exhaustively investigating the fate of all the small polyominoes. Records indicate that he found the switch engine while investigating the decominoes (polyominoes having 10 cells). However, there do not appear to be decominoes which result in a clean switch engine. If Corderman was examining polyominoes in order of size, then this smaller predecessor should have been found first in any case.
Something that looks like a spark, but isn't. An OWSS produces one of these instead of a belly spark, and is destroyed by it.
A non-trivial period-N oscillator contains at least one cell that oscillates at the full period. In other words, it is not made up solely of separate oscillators with smaller periods. Usually it includes a spark or other reaction that would not occur if all lower-period subpatterns were separated from each other, but some exceptions are given under trivial. See also omniperiodic.
A pattern that appears to have an unknown fate due to complex feedback loops, for example involving waves of gliders shuttling between perpendicular rakes. Novelty generator patterns fall short of counting as chaotic growth, since the rakes continue to be predictable, and much of their ash generally remains stable.
It has not been proven conclusively that any particular pattern is in fact an infinite novelty generator, since it is always possible that periodicity will spontaneously arise if the simulation is continued far enough. In fact this happens quite regularly. But conversely, it has not been proven that periodicity must spontaneously arise for all such patterns. Bill Gosper, Nick Gotts and others have done extensive experiments along these lines using Golly.
One of the most common stable edge shooters. This Herschel-to-glider converter suppresses the junk ordinarily left behind by an evolving Herschel while allowing both the first natural glider and second natural glider to escape on transparent lanes:
The complete name for this converter is "NW31T120", where 31 is the output glider lane number. In the above orientation, lane numbers get bigger toward the upper right and smaller toward the lower left (and may easily be negative).
The T120 timing measurement means that a canonical NW glider placed on lane 31 at time T=120, at (+31, +0) relative to the input Herschel, would in theory reach the exact same spacetime locations as the converter's output glider does.
Most converters are not edge shooters and their output lanes are not transparent, so they usually have catalysts that would interfere with this theoretically equivalent glider. This is the case for the optional third glider output created by the lower eater1 catalyst: the upper eater1 overlaps its lane. For the alternate block catalyst suppressing this glider output, see transparent lane.
= NW31
Neither diagonal nor orthogonal. See also knightship.
The first known p5 oscillator, discovered in 1971 independently by Sol Goodman and Arthur Taber. The name is due to the latter.
Found by Robert Wainwright, January 1979.
Any 8-cell polyomino. There are 369 such objects. The word is particularly applied to the following octomino (or its two-generation successor), which is fairly common but lacks a proper name:
Found by Dean Hickerson, August 1989. See also short keys and bent keys.
A cellular automaton is said to be omniperiodic if it has oscillators of all periods. It is not known if Life is omniperiodic, although this seems likely. Dave Buckingham's work on Herschel conduits in 1996 (see My Experience with B-heptominos in Oscillators) left only a short list of unresolved cases, all with periods of 58 or below. The list has been progressively reduced since then. Most recently, period 43 and 53 oscillators were made possible in 2013 by Mike Playle's Snark. As of June 2018, no oscillators are known for periods 19, 23, 38, or 41. If we insist that the oscillator must be non-trivial, then 34 should be added to this list.
Note that if we were to allow infinite oscillators, then all periods are certainly possible, as any period of 14 or more can be obtained using a glider (or LWSS) stream, or an infinitely long 2c/3 wire containing signals with the desired separation.
See grow-by-one object.
A glider synthesis of a spaceship in which all gliders come from the same side of the spaceship's path. Such syntheses are used extensively in the 17c/45 Caterpillar. For example, here is a one-sided way to create an LWSS.
A term used for turners and splitters, specifying that the reaction in question is not repeatable as it would be in a reflector or fanout device. Instead, the constellation is used up, usually in a clean reaction, but the much more common dirty turners and splitters are also very useful in some situations.
For each integer n>1 onion rings of order n is a stable agar of density 1/2 obtained by tiling the plane with a certain 4n × 4n pattern. The tile for order 3 onion rings is shown below. The reader should be able to deduce the form of tiles of other orders.
Any p2 oscillator in which all rotor cells die from overpopulation. The simplest example is a beacon. Compare flip-flop.
Conway's name for the following pentomino, a traffic light predecessor, although not one of the more common ones.
A term proposed by Jason Summers to refer to a natural stabilization of a puffer. For example, the switch engine has two (known) orbits, the block-laying one and the glider-producing one.
Found by Hartmut Holzwart, April 1993.
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Conway's preferred term for a Garden of Eden. According to some definitions, an orphan consists of just the minimum living and dead cells needed to ensure that no parent is possible, whereas a GoE is an entire infinite Life plane that contains an orphan.
A self-constructing spaceship analogous to the Demonoids, with a slow orthogonal direction of travel. The first example was completed by Dave Greene on 29 June 2017, with a top speed of 16c/217251 (this is just 256c/3476016 in lowest terms).
The construction recipe is a stream of MWSSes, with the recovery time limited to 90 ticks by the Lx200 dependent conduit that follows the initial syringe converter. The design is hashlife-friendly, meaning that the spaceship can be trivially adjusted so that spatial and temporal offsets are exact powers of two; period 4194304 and period 8388608 versions have been constructed, with speeds of c/16384 and c/32768 respectively.
The MWSSes are converted to Herschels, which produce a standard single-channel glider stream that runs the Orthogonoid's single construction arm. After the child circuitry is complete, a previously constructed Snark in the parent is removed from the construction arm lane, converting it to a "destruction arm" that shoots down the previous constructor/reflector in the series.
Any pattern that is a predecessor of itself. The term is usually restricted to non-stable finite patterns; period 1 oscillators are stable and are usually just called still lifes. The blinker is the smallest non-stable oscillator, having period 2. There are oscillators of almost all higher periods (see omniperiodic). In general cellular automaton theory the term "oscillator" usually covers spaceships as well, but this usage is not normal in Life.
Oscillators consisting of separate objects which do not react in any phase are usually ignored. For example, a separated blinker and pulsar makes a period 6 oscillator, but is considered trivial.
An oscillator can be divided into a rotor and a stator, and the stator can be further subdivided into bushing and casing. Some oscillators have no casing cells, and a few 100%-volatility oscillators also have no bushing cells.
An oscillator can be constructed from any gun as long as eaters can be added to consume its output. If it is a true gun then the period of the oscillator will be the same as the gun - unless the eating mechanism multiplies the period, as in the case of gliders caught by a boat-bit.
With the discovery of reflectors, relays provide an easy way to create oscillators of all large periods. For example, eight gliders travelling in a loop created by four Snarks can create any period above 42, with a population never exceeding 356 live cells.
For the very lowest periods, whole families of extensible oscillators are known. Examples of this are barberpole, cross, pentoad, p6 shuttle, snacker, and multiple roteightors. Any of the shuttles are oscillators by definition, for example the queen bee shuttle. Many of these are also extensible. Other oscillators such as figure-8 and tumbler have unique mechanisms that are not part of an extended family.
Some oscillators are useful because of the perturbations they can cause to other objects. This is especially true if they provide a spark on their boundary. Some oscillators are explicitly found by search programs in order to produce these sparks, such as pipsquirters.
Some higher period oscillators have been found while running random soups. This is especially true if the soup is run on a cylindrical or torus universe. Sometimes the found objects can be moved to the normal universe and supported there by added catalysts. Achim's p144 is an example.
A pattern constructed by Adam P. Goucher in 2010, which uses an unbounded triangular region as memory for a binary counter. Empty space is read as a zero, and a boat as a one, as shown in the example pattern in memory cell. The pattern's diametric growth rate is O(sqrt(log(t))), which is the slowest possible for any Life pattern, or indeed any 2D Euclidean cellular automaton. The population returns infinitely often to its initial minimum value (during carry operations from 11111...1 to 100000...0, so it can be considered to be an unusual form of sawtooth.
A 2048 × 2048 period 35328 metacell constructed by Brice Due in 2006. It contains a large "pixel" area that contains a large population of LWSSes when the metacell state is ON, but is empty when it is OFF. This allows the state of the metacell to be visible at high zoom levels, unlike previous unit cells where the state was signaled by the presence or absence of a single glider in a specific location.
See natural Heisenburp. Other similar mechanisms, particularly the method of LWSS creation used in the pixel part of the OTCA metapixel, may also be referred to as "out of the blue" reactions.
A term used when a circuit can accept a signal at a specific period which it cannot accept at a higher period. A syringe is a simple example.
Some staged recovery circuits also permit overclocking, and can function successfully at a rate faster than their recovery time. A Silver reflector has a recovery time of 497 ticks, but can be overclocked to reflect a period 250 glider stream, or any nearby period above 248, simply by removing a beehive after the first glider enters the reflector. However, a continuous stream of gliders is then required to maintain the circuit, with timing within a tightly bounded range.
Death of a cell caused by it having more than three neighbours. See also underpopulation.
An important concept in gun and macro-spaceship construction. To be a good candidate for building one of these types of patterns with a new period or speed, a stationary reaction (for a gun) or a moving reaction (for a macro-spaceship) must be able to produce some number of output signals, strictly greater than the number of input signals required to maintain the reaction. The extra signal becomes a gun's output stream, or may be used in a variety of ways to construct the supporting track for a macro-spaceship. By implication, "over-unity" refers to the ratio of output signals to input signals.
If all signal outputs must be used up to sustain a stationary reaction, a high-period oscillator may still be possible. See emu for example.
= OWSS
A would-be spaceship similar to LWSS, MWSS and HWSS but longer. On its own an OWSS is unstable, but it can be escorted by true spaceships to form a flotilla.
A 1976 novel by Piers Anthony which involves Life.
= period
Period 1, i.e., stable. In the context of logic circuitry, this tends to mean that a mechanism is constructed from Herschel conduits that contain only still lifes as catalysts. In the context of slow glider construction, a P1 slow salvo is one in which there are no constraints on the parity of gliders in the salvo, because the intermediate targets are all stable constellations. (The usual alternative is a "P2 slow salvo", where the relative timing between adjacent gliders can be increased arbitrarily, but only by multiples of two ticks.)
A glider gun with period 104, found by Noam Elkies on 21 March 1996. It is based on an R-pentomino shuttle reaction.
A periodic colour-preserving glider reflector with a minimum repeat time of 44 ticks. Unlike the p5 through p8 cases where Noam Elkies' domino-spark based reflectors are available, no small period-22 colour-changing reflector is known. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
In practice this reflector is not useful with input streams below period 121, because lower-period bumpers can be used to reflect all smaller multiples of 11 for which the bumper reaction can be made to work.
A shuttle found in March 2004 by David Eppstein, which originally needed several period 5 oscillators for support. David Bell found a reaction between two of the shuttles to produce a p130 glider gun. On 18 November 2017 Tanner Jacobi found that the stable sidesnagger can be used to support the shuttle instead, and this is shown here.
A glider gun with true period 144. The first one was found by Bill Gosper in July 1994. For a full description and pattern see factory.
A glider gun which emits a period 14 glider stream. This is the smallest possible period for any stream, so such a gun is of great interest. There is no known true-period p14 glider gun, and finding a small direct example is well beyond current search algorithms' abilities. However, pseudo-period p14 guns have been created by injecting gliders into a higher period glider stream. The first pseudo p14 gun was built by Dieter Leithner in 1995. Smaller pseudo p14 guns have since been constructed, but they are still much too large to show here. The essential mechanism used by them is demonstrated in GIG.
Noam Elkies' colour-changing glider reflector, with Karel's p15 providing the necessary domino spark. Compare to the colour-preserving Snark. The minimum repeat time is 30 ticks.
A periodic colour-preserving glider reflector with Karel's p15 providing the necessary spark. The minimum repeat time is 45 ticks. For an equivalent colour-changing periodic glider reflector see p15 bouncer. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
An ambiguous term that may refer to PD-pair reflector, p15 bouncer, or the more recently discovered p15 bumper.
A true period 184 double-barrelled glider gun found by Dave Buckingham in July 1996. The engine in this gun is a Herschel descendant. Unlike previous glider guns, the reaction flips on a diagonal so that both gliders travel in the same direction.
A metacell constructed by Adam P. Goucher in 2008, capable of being programmed to emulate any Moore neighborhood rule, including isotropic and anisotropic non-totalistic rules. It fits in a 32768 by 32768 bounding box, with the resulting metacell grid at 45 degrees to the underlying Life grid. Like the OTCA metapixel, it includes a large "pixel" area so that the state of the megacell can easily be seen even at extremely small-scale zoom levels.
A variant of Jason Summers' telegraph pattern, constructed in 2010 by Adam P. Goucher using only stable circuitry. A single incoming glider produces the entire ten-part composite lightspeed signal that restores the beehive-chain lightspeed wire to its original position. The signal is detected at the other end of the telegraph and converted back into a single output signal. This simplification came at the cost of a much slower transmission speed, one bit per 91080 ticks. In this mechanism, sending the entire ten-part signal constitutes a '1' bit, and not sending the signal means '0'. See also high-bandwidth telegraph.
A true period 22 glider gun constructed by David Eppstein in August 2000, using two interacting copies of a p22 oscillator found earlier the same day by Jason Summers.
A true period glider gun with period 246, discovered by Dave Buckingham in June 1996. The 180-degree mod-123 symmetry of its bookend-based engine makes it trivial to modify it into a double-barrelled gun. Its single-barreled form is shown below.
A glider gun with true period 24. The first one was found by Noam Elkies in June 1997. It uses three p4 oscillators to hassle a pair of traffic lights. One of the oscillators was very large and custom-made. Shown below is a much smaller version built by Jason Summers and Karel Suhajda in December 2002, using the same mechanism but with a smaller oscillator:
A true period 256 four-barrelled glider gun found by Dave Buckingham in September 1995. It uses four R64 conduits to make the second smallest known Herschel loop (after the Simkin glider gun). The p256 gun was an early "teaser" from Dave Buckingham before he released his full Herschel technology.
A hassler where two copies of a period 29 oscillator (which is itself a pre-pulsar hassler) change the period of a pentadecathlon.
A glider gun with true period 30. The first one, found by Bill Gosper in November 1970 (see Gosper glider gun), was also the first gun found of any period. All known p30 glider guns are made from two or more interacting queen bee shuttles. Paul Callahan found 30 different ways that three queen bee shuttles can react to form a period 30 glider gun. One of the most interesting of these is shown below in which the gliders emerge in an unexpected direction.
= buckaroo
A glider gun with true period 36. The first one was found by Jason Summers in 2004. Shown below is a smaller version using improvements by Adam P. Goucher and Scot Ellison:
A variant of Tanner Jacobi's bumper found by Arie Paap in April 2018. Two forms of the period 3 oscillator catalyst are shown below.
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For bounding box optimization purposes, it's also possible to replace the eater1 in a p3, p6 or p9 bumper with another period 3 oscillator, saving one row along the south edge at the cost of a higher population.
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The repeat time for all these variants is 36 ticks, as shown.
A glider gun with a true period of 44. The first one was found by Dave Buckingham in April 1992. It uses two interacting copies of an oscillator which he also found. In 1996 he found a gun which only used one copy of the oscillator. Paul Callahan improved it in 1997, resulting in the gun shown below:
A gun discovered by Dieter Leithner in April 1997, in a somewhat larger form. This was the smallest known gliderless gun and smallest known MWSS gun until the construction in 2017 of the gun shown under gliderless, based on Tanner's p46.
The p44 MWSS gun is based on a p44 oscillator discovered by Dave Buckingham in early 1992, shown here in an improved form found in January 2005 by Jason Summers using a new p4 sparker by Nicolay Beluchenko. A glider shape appears in this gun for three consecutive generations, but always as part of a larger cluster, so even a purist would regard this gun as gliderless.
A true-period glider gun discovered by Matthias Merzenich in April 2010. By most measures this is the smallest known odd-period gun of any type, either true-period or pseudo-period:
A glider gun which has true-period 46. The first one found was the new gun by Bill Gosper in 1971. Prior to the discovery of Tanner's p46 in October 2017, all known p46 guns were made from two or more twin bees shuttles that interact (e.g., see twin bees shuttle pair). See edge shooter and double-barrelled for two more of these.
On 21 October 2017 Heinrich Koenig found a glider gun using two copies of Tanner's p46 placed at right angles to each other. This is the first p46 gun found which makes no use of the twin bees shuttle.
See gliderless for a MWSS gun also made using two copies of Tanner's p46.
A true period compound glider gun based on the p24 gun, using a Rich's p16 oscillator as a filter to remove half of the gliders from the stream.
A periodic colour-preserving glider reflector with a minimum repeat time of 36. Unlike the p5 through p8 cases where Noam Elkies' domino spark-based reflectors are available, no small period-4 colour-changing reflector is known. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
The following glider reflector, discovered by Karel Suhajda in October 2012. Its minimum repeat time is 52 ticks. Unlike the various bouncers discovered many years earlier, it is a colour-preserving reflector, so it was made obsolete the following year by the discovery of the much smaller stable Snark, which uses the same initial bait reaction and so produces an output glider with the same timing. For a smaller periodic colour-preserving glider reflector with a different output timing, see p4 bumper.
A surprising variant of the twin bees shuttle found by Dave Buckingham in 1973. See also centinal.
A colour-changing glider reflector constructed by Noam Elkies in September 1998 by welding together two special-purpose period-5 sparkers. The minimum repeat time is 25 ticks. For colour-preserving glider reflectors see p5 bumper and the stable Snark reflector.
A periodic colour-preserving glider reflector with a middleweight volcano producing the necessary spark. The minimum repeat time is 35 ticks. For an equivalent colour-changing periodic glider reflector see p5 bouncer. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
Traditional name for p5 bouncer before 2016, but with the discovery of the p5 bumper this has become an ambiguous reference.
A glider gun with a true period of 60. The first one was found by Bill Gosper in 1970 and is shown below.
A true period 690 glider gun found by Noam Elkies in July 1996. It is composed of a p30 queen bee shuttle pair and a p46 twin bees shuttle whose sparks occasionally react with each other. This is a very compact gun for such a high period and is used in many patterns requiring sparse glider streams.
Noam Elkies' colour-changing glider reflector using the p6 pipsquirter, with a minimum repeat time of 24 ticks. For colour-preserving glider reflectors see p6 bumper and the stable Snark reflector.
A periodic colour-preserving glider reflector with a unix providing the necessary spark. The minimum repeat time is 36 ticks. For an equivalent colour-changing periodic glider reflector see p6 bouncer. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
A pipsquirter oscillator found by Noam Elkies in November 1997, used in various hasslers and the colour-changing p6 bouncer.
Traditional name for p6 bouncer before 2016, but with the discovery of the p6 bumper this has become an ambiguous reference.
The following oscillator found by Nicolay Beluchenko in February 2004.
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The following oscillator, found by Jason Summers in August 2005. Although this looks at first sight like a shuttle, it isn't really.
Noam Elkies' colour-changing glider reflector using a p7 pipsquirter, with a minimum repeat time of 28 ticks. A high-clearance version is shown in p7 pipsquirter. For colour-preserving glider reflectors see p7 bumper and the stable Snark reflector.
A periodic colour-preserving glider reflector with a minimum repeat time of 35 ticks. For an equivalent colour-changing periodic glider reflector see p7 bouncer. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
A pipsquirter oscillator found by Noam Elkies in August 1999, used in various hasslers and the colour-changing p7 reflector.
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A larger period-7 pipsquirter is used in cases where space is limited where the reflector should extend southward for as short a distance as possible:
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Traditional name for p7 bouncer before 2016, but with the discovery of the p7 bumper this has become an ambiguous reference.
A glider reflector constructed by Noam Elkies in September 1998, with a minimum repeat time of 24 ticks. It is a constellation containing a figure-8, boat, eater1, and block. For colour-preserving glider reflectors see p8 bumper and the stable Snark reflector.
A periodic colour-preserving glider reflector with a blocker attached to provide the necessary spark. The minimum repeat time is 40 ticks. For an equivalent colour-changing periodic glider reflector see p8 bouncer. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
A small periodic variant of a stable two-glider-to-Herschel component found by Paul Callahan in November 1998 and used in the Callahan G-to-H, Silver reflector and Silver G-to-H. The minimum repeat time is 192 ticks, though some lower periods such as 96 are possible via overclocking. Here a ghost Herschel marks the output signal location:
Traditional name for p8 bouncer before 2016, but with the discovery of the p8 bumper this has become an ambiguous reference.
A glider gun with true period 90. The one below by Dean Hickerson uses the output of two p30 guns in a period-multiplying reaction:
A glider gun with a true period of 92. The first one was found by Bill Gosper in 1971 using a period doubling reaction using two p46 guns. Many different p92 guns are known that use multiple twin bees shuttles. A period 92 gun can also be made by adding a semi-cenark to any period 46 glider gun.
On 18 November 2017, Martin Grant found a new gun using one twin bees shuttle and one Tanner's p46 oscillator, making it the smallest known p92 gun.
A periodic colour-preserving glider reflector with a repeat time of 36. Unlike the p5 through p8 cases where Noam Elkies' domino spark-based reflectors are available, no small period-9 colour-changing reflector is known. A stable Snark reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider streams.
= bookends
A relatively 180-degree rotationally symmetric 14-bit still life. The Iwona methuselah contains a paperclip in its ash.
A much smaller successor to the half-baked knightship, constructed by Chris Cain in September 2014. Several slow-salvo recipes are needed to support the multi-glider salvo seeds at the upstream end of the spaceship. "Parallel" means that these recipes are sent in parallel instead of one after the other, in series, as in the original HBK.
An armless constructor pattern that is programmed to build Parallel HBK oblique spaceships every 125906944 ticks. This gun was created by Chris Cain on 3 January 2015.
A self-sustaining reaction attached to the output of a rake or puffer, that damages or modifies the standard output. Compare tagalong. In 2009, while experimenting with novelty generator patterns in Golly, Mitchell Riley discovered parasites on glider streams from p20 and p8 backward rakes. In some cases, parasites can even "reproduce", as in the pattern below, though the number of copies is limited since they will eventually use up their host glider stream:
A pattern is said to be a parent of the pattern it gives rise to after one generation. Some patterns have infinitely many parents, but others have none at all (see Garden of Eden). Typically parents are considered trivial if they contain groups of cells that can be removed without changing the result, such as isolated faraway cells.
The three cells that cause a new cell to be born.
Even or odd, particularly as applied to the phase of an oscillator or spaceship. For example, in slow salvo constructions, the intermediate targets are frequently period 2, most often because they contain blinkers or traffic lights. A glider striking a P2 constellation will generally produce a different result depending on its parity. Period-4 intermediate targets are rare (or not used), so it doesn't matter for example whether an odd-parity glider in a slow salvo is phase 1 or phase 3. Only the even/odd parity is important.
An intermediate object found by a search program which might be a substantial part of a complete spaceship or oscillator, but which isn't complete.
Running a partial result works for a few generations until the speed of light corruption from any unfinished edge destroys the whole object. But a partial result can still be used to see whether the object (if ever finished) would provide a desired spark or perturbation. If no partial results are found then it is likely that no such object exists under the constraints of the search.
Very large partial results can indicate that there is a good chance that the object being searched for might actually exist (but this is no guarantee). Rerunning the search using the partial result as a base and relaxing some constraints, widening or adjusting the search area, or splitting the object into multiple arms might result in finding a complete working object.
As an example, here is a large partial result for a period 6 knightship found by Josh Ball in April 2017. The first 22 columns were rediscovered in 2018 as part of the successful search for Sir Robin. See also almost knightship for an earlier small example by Eugene Langvagen.
A pair of pentadecathlons arranged so that their V sparks turn a glider by 90 degrees. The minimum repeat time is 45 ticks.
An oscillator found by Dave Buckingham in 1973.
Found by Dave Buckingham, 1972.
Found in 1970 by Conway while tracking the history of short rows of cells, 10 cells giving this object, which is the most natural oscillator of period greater than 3. In fact it is the fifth most common oscillator overall, appearing in random soups slightly more frequently than the clock, but much less frequently than the blinker, toad, beacon or pulsar. The pentadecathlon can be constructed using just three gliders, as shown in glider synthesis.
The pentadecathlon is the only known oscillator that has two phases that are different polyominoes. It produces accessible V sparks and domino sparks, which give it a great capacity for doing perturbations, especially for period 30 based technology. See relay for example.
Found by Dave Buckingham, July 1976.
Any 5-cell polyplet.
The barberpole of length 5.
Found by Bill Gosper, June 1977. This is extensible: if an eater is moved back four spaces then another Z-hexomino can be inserted. (This extensibility was discovered by Scott Kim.)
Any 5-cell polyomino. There are 12 such patterns, and Conway assigned them all letters in the range O to Z, loosely based on their shapes. Only in the case of the R-pentomino has Conway's label remained in common use, but all of them can nonetheless be found in this lexicon.
The smallest number of generations it takes for an oscillator or spaceship to reappear in its original form. The term can also be used for a puffer, wick, fuse, superstring, stream of spaceships, factory or gun. In the last case there is a distinction between true period and pseudo period. There is also a somewhat different concept of period for wicktrailers.
See period multiplier.
For circuit mechanisms, "periodic" is the opposite of p1 or stable. Periodic circuits necessarily contain oscillators, and therefore they can generally only accept input signals that are synchronized to the combined period of those oscillators (but see universal regulator).
For signal streams, "periodic" means that signals will only be present in the stream at one out of every n ticks, where n is the period of the stream. In a periodic intermittent stream there may be gaps, so that signals do not always appear at every nth tick. However, if a signal does appear, its distance measured in ticks from previous and future signals will always be an exact multiple of n.
A term commonly used for a pulse divider, because dividing the number of signals in a regular stream by N necessarily multiplies the period by N. The term "period multiplier" can be somewhat misleading in this context, because most such circuits can accept input streams that are not strictly periodic.
Reactions have also been found to period double or period triple the output of some rakes to create high-period rakes in a relatively small space (i.e., an exponential increase in period for a linear increase in size).
For Herschel signals and glider guns, a number of small period doubler, tripler, and quadrupler mechanisms are known. For example, the following conduit produces one output glider after accepting four input B-heptominoes, or four Herschels if a conduit such as F117 is prepended that includes the same BFx59H converter.
See semi-Snark and tremi-Snark for additional examples using glider streams. As of June 2018 no stable period-multiplying elementary conduits are known for a multiplication factor of five or higher, though it is easy to construct composite ones.
A signal-carrying circuit that can be modified so that it cleanly absorbs any future signals instead of allowing them to pass. Optionally there may be a separate mechanism to restore the circuit to its original function.
In the following example, a glider from the northeast (shown) will perform a simple block pull that switches off an F166 conduit, so that any future Herschel inputs will be cleanly absorbed. A glider from the southwest (also shown) can restore the block to its original position.
To change the fate of an object by reacting it with other objects. Typically, the other objects are sparks from spaceships or oscillators, or are eaters or impacting spaceships. Perturbations are typically done to turn a dirty reaction into a clean one, or to change the products of a reaction. In many desirable cases the perturbing objects are not destroyed by the reaction, or else are easily replenished.
= perturb.
One of the three elementary conduits used in the composite Fx176 Herschel conduit. It converts an input pi-heptomino into an output wing in 35 ticks. In November 2017, Aidan F. Pierce discovered the compact PF35W variant below, which improved the repeat time of the Fx176 to 73 ticks and allowed gliders from following dependent conduits to escape freely:
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A representative generation of a periodic object such as an oscillator or spaceship. The number of phases is equal to the period of the object. The phases of an object usually repeat in the same cyclic sequence forever, although some perturbations can cause a phase change.
A perturbation of a periodic object that causes the object to skip forward or backward by one or more phases. If the perturbation is repeated indefinitely, this can effectively change the period of the object. An example of this, found by Dean Hickerson in November 1998, is shown below. In this example, the period of the oscillator would be 7 if the mold were removed, but the period is increased to 8 because of the repeated phase changes caused by the mold's spark.
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The following pattern demonstrates a p4 c/2 spaceship found by Jason Summers, in which the phase is changed as it deletes a forward glider. This phase change allows the spaceship to be used to delete a glider wave produced by a rake whose period is 2 (mod 4).
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Phase changing reactions have enabled the construction of spaceships having periods that were otherwise unknown, and also allow the construction of period-doubling and period-tripling convoys to easily produce very high period rakes.
See also blinker puffer.
The following common spark. The name comes from the shape in the generation after the one shown here.
See pi calculator.
Any pattern all of whose cells die in every generation, but which never dies as a whole. A spaceship cannot be a phoenix, and in fact every finite phoenix eventually evolves into an oscillator. The following 12-cell oscillator (found by the MIT group in December 1971) is the smallest known phoenix, and is sometimes called simply "the phoenix".
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An easy synthesis of the phoenix is possible using four blocks as seeds. A puffer creating a growing row of phoenixes has the unusual property that the percentage of live cells that stay alive for more than one generation approaches zero. See lone dot agar for an example of an infinite phoenix.
A series of patterns by Paul Tooke in 2010, based on a simplification and extension of the Gemini spaceship's construction mechanism. Tooke produced a number of slow-salvo-constructed patterns with superlinear growth, including a series of breeder patterns of previously unknown types. For some patterns, the Gemini's two construction arms were moved to a permanent stationary platform, using fourteen glider-loop channels instead of twelve.
Some of these breeder patterns remain difficult to classify unambiguously. For example, one pattern was designed to be an MSS breeder - a modified Gemini spaceship puffing slide guns which build lines of blocks. However, the slide guns produce both moving and stationary objects at a linear rate, because streams of gliders are needed to reach out to the construction zone to do the push reaction and build more blocks. The pattern could therefore be classified as a hybrid MSM/MSS breeder. Other breeder patterns utilizing slide guns and universal constructor technology are likely to cause similar classification ambiguities.
A device constructed by Adam P. Goucher in February 2010, which calculates the decimal digits of pi (the transcendental number, not the Life pattern!) and displays them in the Life universe as 8×10 dot matrix characters formed by arrangements of blocks along a diagonal stripe at the top. A push reaction moves a ten-block diagonal cursor to the next position as part of the "printing" operation for each new digit.
The actual calculation is done in binary, using a streaming spigot algorithm based on linear fractional transformations. The pi calculator is made up of a 188-state computer connected to a printing device via period-8 regulators and a binary-to-decimal conversion mechanism. The complete pattern can be found in Golly's Very Large Patterns online archive, along with the very similar 177-state phi calculator which uses a simpler algorithm to calculate and print the Golden Ratio.
The reaction that defines rate of travel of the Caterpillar spaceship. A pi climber consists of a pi-heptomino "climbing" a chain of blinkers, moving 17 cells every 45 ticks, and leaving behind an identical chain of blinkers, shifted downward by 6 cells. A single pi climber does not produce any gliders or other output, but two or more of them travelling on nearby blinker chains can be arranged to emit gliders every 45 ticks. Compare Herschel-pair climber.
A common pattern. The name is also applied to later generations of this object. In a pi ship, for example, the pi-heptomino itself never arises.
Found by Simon Norton, April 1970. Compare clock II.
Found by Noam Elkies, August 1995. In this oscillator, a pi-heptomino is turned ninety degrees every 42 generations. A second pi can be inserted to reduce the period to 84.
Found by Robert Wainwright in 1984 or 1985. Compare with gourmet and popover.
An oscillator that produces a domino spark that is orientated parallel to the direction from which it is produced (in contrast to domino sparkers like the pentadecathlon and HWSS, which produce domino sparks perpendicular to the direction of production). See p6 pipsquirter, p7 pipsquirter.
A growing spaceship in which the back part consists of a pi-heptomino travelling at a speed of 3c/10. The first example was constructed by David Bell. All known pi ships are too large to show here, but the following diagram shows how the pi fuse works.
Found in 1971.
A line of pi-heptominoes stabilizing one another. For example, an infinite line of pi-heptominoes arranged as shown below produces a pi wave that moves at a speed of 3c/10 with period 30, and leaves no debris.
= cell
= polyplet
A finite collection of orthogonally connected cells. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of Life and other cellular automata involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life. (Note on spelling: As with "dominoes" the plural may also be spelt without an e. In this lexicon I have followed Golomb in using the longer form.)
It is possible for a polyomino to be an oscillator. In fact there are infinitely many examples of such polyominoes, namely the cross and its larger analogues. The only other known examples are the block, the blinker, the toad, the star and (in two different phases) the pentadecathlon.
A polyomino can also be a spaceship, as the LWSS, MWSS and HWSS show.
A finite collection of orthogonally or diagonally connected cells. This king-wise connectivity is a more natural concept in Life than the orthogonal connectivity of the polyomino.
This term is often used to mean bi-pond, but may also be used of the following pseudo still life.
Found by Robert Wainwright in August 1984. Compare with gourmet and pi portraitor.
The number of ON cells.
Conway's name for the following pentomino, a common spark.
A pre-pulsar spaceship. Any of three different p30 c/5 orthogonal spaceships in which a pre-pulsar is pushed by a pair of spiders. The back sparks of the spaceship can be used to perturb gliders in many different ways, allowing the easy construction of c/5 puffers. The first PPS was found by David Bell in May 1998 based on a p15 pre-pulsar spaceship found by Noam Elkies in December 1997. See also SPPS and APPS.
The pattern below shows the basic mechanism of a PPS. The two isolated sparks at the left and right sides are the edge sparks from the two supporting spiders.
The following common parent of the beehive.
The following common parent of the block. Another such pattern is the grin.
Any pattern that evolves into a given pattern after one or more generations.
A common predecessor to the pre-block (and thus the block):
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A common predecessor of the pulsar, such as that shown below. This duplicates itself in 15 generations. (It fails, however, to be a true replicator because of the way the two copies then interact.)
A pair of tubs can be placed to eat half the pre-pulsar as it replicates; this gives the p30 oscillator Eureka where the pre-pulsar's replication becomes a movement back and forth. See twirling T-tetsons II for a variation on this idea. By other means the replication of the pre-pulsar can be made to occur in just 14 generations as half of it is eaten; this allows the construction of p28 and p29 oscillators. The pre-pulsar was also a vital component of the first known p26 and p47 oscillators.
See also PPS.
= PPS.
Found by the MIT group in September 1971. Compare mini pressure cooker.
A pattern originally constructed by Dean Hickerson in November 1991 that emits a stream of LWSSs representing the prime numbers. Some improvements were found by Jason Summers in October 2005.
Found by Dave Buckingham, November 1972.
Opposite of true. A gun emitting a period n stream of spaceships (or rakes) is said to be a pseudo period n gun if its mechanism oscillates with a period greater than n. This period will necessarily be a multiple of n. If the base mechanism's period is instead a fraction of n, then a period multiplier must also be present which is considered to be part of the mechanism, and the gun as a whole is still a true period gun. For example, a filter may be used on a lower-period gun to produce a compound gun such as the true p48 gun.
Pseudo period n glider guns are known to exist for all periods greater than or equal to 14, with smaller periods being impossible. All known p14 guns are pseudo guns requiring several signal injections, so they are quite large. The following smaller example is a pseudo period 123 gun, interleaving the streams from two true period 246 guns:
The same distinction between true and pseudo also exists for puffers.
Found by Achim Flammenkamp in August 1994. In terms of its minimum population of 15 this is the smallest known p5 oscillator. See also barberpole.
A pseudo-random number generator in which the bits are represented by the presence or absence of gliders. The first pseudo-random glider generator was built by Bill Gosper. David Bell built the first moving one in 1997, using c/3 rakes.
A pseudo-random number generator (PRNG) is an algorithm that produces a sequence of bits that looks random (but cannot really be random, being algorithmically determined).
In Life, the term refers to a PRNG implemented as a Life pattern, with the bits represented by the presence or absence of objects such as gliders or blocks. Such a PRNG usually contains gliders or other spaceships in a loop with a feedback mechanism that causes later spaceships to interfere with the generation of earlier spaceships. The period can be very high, as a loop of n spaceships has 2n possible states.
A stable pattern whose live cells are either immediately adjacent to each other, or are connected into a single group by adjacent dead cells where birth is suppressed by overpopulation.
The definition of strict still life rules out such stable patterns as the bi-block. In such patterns there are dead cells which have more than 3 neighbours in total, but fewer than 3 in any component still life. These patterns are called pseudo still lifes, and have been enumerated up to 32 bits, as shown in the table below.
-------------- Bits Number -------------- 8 1 9 1 10 7 11 16 12 55 13 110 14 279 15 620 16 1645 17 4067 18 10843 19 27250 20 70637 21 179011 22 462086 23 1184882 24 3068984 25 7906676 26 20463274 27 52816265 28 136655095 29 353198379 30 914075620 31 2364815358 32 6123084116 --------------
Attribution of these counts is given in strict still life; see also https://oeis.org/A056613. The unique 32-bit triple pseudo still life is included in the last count in the table. As the number of bits increases, the pseudo still life count goes up exponentially by approximately O(2.56n). By comparison, the rate for strict still lifes is about O(2.46n) while for quasi still lifes it's around O(3.04n).
If a stable pattern's live cells plus its overpopulated dead cells do not form a single mutually adjacent group, the pattern is usually referred to as a constellation. It is also a still life in the general sense, but is neither "pseudo" nor "strict".
An object that moves like a spaceship, except that it leaves debris behind. The first known puffers were found by Bill Gosper and travelled at c/2 orthogonally (see diagram below for the very first one, found in 1971).
Not long afterwards c/12 diagonal puffers were found (see switch engine). Discounting wickstretchers, which are not puffers in the conventional sense, no new velocity was obtained after this until David Bell found the first c/3 orthogonal puffer in April 1996. Other new puffer speeds followed over the next several years.
Many spaceships that travel orthogonally at a speed less than c/2 have useful side or back sparks. These can be used to perturb standard spaceships that approach from behind. A common technique for creating puffers for a new speed uses a convoy of the new spaceships to create debris from an approaching standard spaceship such that a new standard spaceship is recreated on the same path as the original one. This forms a closed loop, resulting in a high-period puffer for the new speed.
As of June 2018, puffers have been found matching every known velocity of elementary spaceship, except for c/6 and c/7 diagonal and (2,1)c/6. It is also generally easy to create puffers based on macro-spaceships, simply by removing some part of the trailing cleanup mechanism.
A pattern which can be used as the main component of a puffer. The pattern may itself be a puffer (e.g. the classic puffer train), it may be a spaceship (e.g. the Schick engine), or it may even be unstable (e.g. the switch engine).
A puffer discovered by Richard Schank in November 2014, from a symmetric soup search using an early version of apgsearch. It consists of a pair of B-heptominoes stabilised by a backend that leaves only pairs of blocks behind. It is simple enough to be easily synthesized with gliders.
Generally, any spaceship constructed using pufferfish. May refer specifically to the extensible c/2 spaceship constructed by Ivan Fomichev in December 2014, the first such spaceship to contain no period-2 or period-4 parts. (The first two or three rows might be considered to be period 2 or 4, but they are directly dependent on following rows for support.).
The pattern consists of two adjacent pufferfish puffers, plus four copies of a nontrivial period 36 c/2 fuse for pufferfish exhaust, discovered using a randomized soup search.
The full name for a puffer, coined by Conway before any examples were known. The term was also applied specifically to the classic puffer train found by Bill Gosper and shown below. This is very dirty, and the tail does not stabilize until generation 5533. It consists of a B-heptomino (shown here one generation before the standard form) escorted by two LWSS. (This was the second known puffer. The first is shown under puffer.)
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An attachment at the back of a line puffer that suppresses all or some of its puffing action. The example below (by Hartmut Holzwart) has a 3-cell puff suppressor at the back which suppresses the entire puff, making a p2 spaceship. If you delete this puff suppressor then you get a p60 double beehive puffer. Puff suppressors were first recognised by Alan Hensel in April 1994.
A reaction, most often mediated by gliders, that moves an object closer to the source of the reaction. See block pull, blinker pull, loaf pull; also elbow.
Despite its size, this is the fourth most common oscillator (and by far the most common of period greater than 2) and was found very early on by Conway. See also pre-pulsar, pulsar quadrant, and quasar.
= pulsar (The numbers refer to the populations of the three phases.)
A large-scale raster line display device constructed by Mark Walsh in August 2010, where pulsars form the individual pixels in an otherwise empty grid. The published sample pattern displays and erases eight 7×5-pixel characters on each of two lines of text.
This consists of a quarter of the outer part of a pulsar stabilized by a cis fuse with two tails. This is reminiscent of mold and jam. Found by Dave Buckingham in July 1973. See also two pulsar quadrants.
A moving object, such as a spaceship or Herschel, which can be used to transmit information. See pulse divider.
Also another name for a pulsar quadrant.
A mechanism that lets every n-th object that reaches it pass through, and deletes all the rest, where n > 1 and the objects are typically gliders, spaceships or Herschels. A common synonym is period multiplier. For n=2, the simplest known stable pulse dividers are the semi-Snarks.
The following diagram shows a p5 glider pulse divider by Dieter Leithner (February 1998). The first glider moves the centre block and is reflected at 90 degrees. The next glider to come along will not be reflected, but will move the block back to its original position. The relatively small size and low period of this example made it useful for constructing compact glider guns of certain periods, but it became largely obsolete with the discovery of the stable CC semi-Snark, which uses the same basic mechanism. Period 7, 22, 36 and 46 versions of this pulse divider are also known.
Found by Robert Wainwright, May 1985. Compare Eureka.
A pattern that evolves into one or more gliders, and nothing else. There was some interest in these early on, but they are no longer considered important. Here's a neat example:
A reaction that moves an object farther away from the source of the reaction. See sliding block memory, pi calculator, elbow, universal constructor. See also pull, fire.
Any tagalong at the front of a spaceship. The following is an example found by David Bell in 1992, attached to the front of a MWSS.
Found by Dave Buckingham in 1972.
A common mistaken spelling of pyrotechnecium, caused by a copying error in the early 1990s.
= Quetzal
Abbreviation for quarter diagonal.
Conway's name for the following pentomino, a traffic light predecessor.
Found by Robert Kraus, April 1971. Of all oscillators that fit in a 6×6 box this is the only flipper.
A form of colourised Life in which there are four types of ON cell. A newly-born cell takes the type of the majority of its three parent cells, or the remaining type if its parent cells are all of different types. In areas where there are only two types of ON cell QuadLife reduces to Immigration.
The barberpole of length 4.
A still life that can be broken down into four stable pieces but not into two or three. This term may refer to the following 34-bit pattern, found by Gabriel Nivasch in July 2001, or any similar pattern with the same property.
As a consequence of the Four-Colour Theorem, there can be no analogous objects requiring decomposition into five or more pieces. By convention, patterns like this and the triple pseudo are considered to be pseudo still lifes, not strict still lifes. As of June 2018, it has been shown that no quad pseudo patterns exist with 32 or fewer bits, but a 33-bit pattern with this property may theoretically still be found.
A toolkit developed by Dean Hickerson and Gabriel Nivasch in 2006, enabling the construction of patterns with asymptotic population growth matching an infinite number of different sublinear functions - namely, O(t(1/2n)) for any chosen n. See also exponential filter, recursive filter.
The fastest possible asymptotic rate of population growth for any Life pattern - O(t2) in big-O notation, where t is the number of ticks. The first quadratic-growth pattern found was Bill Gosper's 1971 breeder. Many other types of breeders and spacefillers have been constructed since.
In April 2011, Stephen Silver gave an example of a one-cell-thick pattern over a million cells long that exhibited quadratic growth. In October 2015, Chris Cain constructed a one-cell-thick pattern with a reduced bounding box of 2596×1, improving on a series of previous longer results. The smallest known quadratic growth pattern by initial population is the 23-cell switch-engine ping-pong by Michael Simkin.
There are an infinite number of possible growth rates between linear and quadratic growth. See superlinear growth.
A pattern that fills all or part of the Life plane by making copies of itself in a nonlinear way. Small quadratic replicators are known in other Life-like rules, but as of July 2018 no example has been found or constructed in Conway's Life.
Any sawtooth pattern with a quadratic envelope, or specifically a pattern assembled by Martin Grant in May 2015, consisting of two caber tossers with period multipliers for timing which activate and deactivate two toggleable rake guns (see toggleable gun). The gliders emitted by those rakes annihilate on the diagonal while the rakes are eaten by 2c/5 ships. All the rakes and gliders are destroyed before the next cycle. See also Osqrtlogt.
A period-multiplying colour-preserving signal conduit found by Tanner Jacobi in October 2017, producing one output glider for every four input gliders. It is made by replacing one of the eaters in a tremi-Snark with a catalyst found using Bellman. The catalyst causes the formation of a tub which then requires an additional glider to delete. However, this adds 5 ticks to the repeat time, so that it becomes 48. If period quadrupling is needed with a colour-changing reaction, a CP semi-Snark and a CC semi-Snark can be used in series, or a period-multiplying Herschel conduit can be connected to a syringe and an appropriately chosen Herschel-to-glider converter.
= quadpole
The following spaceship, found by Jason Summers in September 2000. The name is due to the 25-cell minimum population. This is the smallest known c/4 spaceship other than the glider. This spaceship can also be used to make the smallest known tubstretcher.
A unit of measurement sometimes used for diagonal distances, especially for slow salvo glider lanes. One advantage of measurement in quarter diagonals is that gliders travel diagonally at 1qd/tick, so that the same integer value can serve as either a time or a diagonal distance measurement.
Found by Robert Wainwright, August 1971. This is related to the pulsar, and is just the smallest of an extensible series of p3 oscillators built using pulsar quadrants which are shifted with respect to each other.
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A stable constellation where the individual still lifes share dead cells, so the neighborhoods of those dead cells are changed, but all cells that used to remain dead from under-population still do so. Under Life rules, this occurs when objects are diagonally adjacent (e.g., two blocks sharing a single diagonal neighbor) or when single protruding cells in two objects such as tubs share multiple neighbors. The term is due to Mark Niemiec.
---------------- Bits Count ---------------- 8 6 9 13 10 57 11 141 12 465 13 1224 14 3956 15 11599 16 36538 17 107415 18 327250 19 972040 20 2957488 21 8879327 22 26943317 ----------------
As the number of bits increases, the quasi still life count goes up exponentially by approximately O(3.04n), slightly more than a factor of three. By comparison, the rate for strict still lifes is about O(2.46n) while for pseudo still lifes it's around O(2.56n).
See queen bee shuttle.
Found by Bill Gosper in 1970. There are a number of ways to stabilize the ends. Gosper originally stabilized shuttles against one another in a square of eight shuttles. Two simpler methods are shown here; for a third see buckaroo. The queen bee shuttle is the basis of all known true p30 guns (see Gosper glider gun).
Any arrangement of two queen bee shuttles such that the two beehives created between them are consumed in some way. There are many ways that the two shuttles can be placed, either head-to-head, or else at right angles. The most well-known and useful arrangement results in the Gosper glider gun.
Other arrangements don't create any lasting output, but create large sparks which can perturb objects (especially gliders) in various ways. For example, one arrangement of a queen bee shuttle pair was used in the original unit Life cell as a memory cell. Here an input glider is converted into a block, which remains until it is deleted by a glider on a right-angled path.
Any Herschel track-based gun with a period below 62, which is the lowest period with a stable glider-emitting conduit. This was Dieter Leithner's name for the true p54 glider gun he built in January 1998 - a short form of Quetzalcoatlus, which expresses the fact that the gun was a very large Herschel loop that was not an emu. Shortly afterwards Leithner also built a p56 Quetzal using a mechanism found by Noam Elkies for this purpose. In October 1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5 reflector of the previous month. Quetzals of periods 57-61 have since been constructed.
Some of the more recent Quetzals are not Herschel loops, but are instead short Herschel tracks firing several glider streams all but one of which is reflected back to the beginning of the track to create a new Herschel. Noam Elkies first had the idea of doing this for the p55 case, and Stephen Silver constructed the resulting gun shortly after building the original (much larger) p55 Quetzal. Jason Summers later built a p54 version, which is more complicated because the evenness of the period makes the timing problems considerably more difficult.
A giant flying dinosaur after which Dieter Leithner named his p54 gun. Usually abbreviated to Quetzal, or simply Q (as in Q54, Q55, Q56, Q-gun, etc.).
A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in July 1996. It is made up of two elementary conduits, HRx131B + BFx59H. After 190 ticks, it produces a Herschel turned 90 degrees clockwise at (24, 16) relative to the input. Its recovery time is 107 ticks. A ghost Herschel in the pattern below marks the output location:
This was found, in the form shown below, by Peter Raynham in the early 1970s. The name derives from a form with a larger and less symmetric stator found by Noam Elkies in August 1994. Compare with Gray counter.
An elementary conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in September 1995. After 64 ticks, it produces a Herschel rotated 90 degrees clockwise at (11, 9) relative to the input. Its recovery time is 153 ticks, though this can be improved to 61 ticks by adding a from-the-side eater inside the turn to avoid interference from the output Herschel's first natural glider, as shown below. A ghost Herschel in the pattern below marks the output location:
A 9-cell methuselah found by Andrew Trevorrow in 1986.
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A pattern in which a signal makes its way in a loop through an "obstacle course" of reactions in order to demonstrate various ways that the signal can be reflected, temporarily stored, and converted. The more different reactions that are used the better the racetrack. David Goodenough built racetracks for p30 and p46 technology in 1995. Racetracks are also known for Herschel conduit technology, and simple ones are useful for building oscillators and glider guns.
Any puffer whose debris consists of spaceships. A rake is said to be forwards, backwards or sideways according to the direction of the spaceships relative to the direction of the rake. Originally the term "rake" was applied only to forwards c/2 glider puffers (see space rake). Many people prefer not to use the term in the case where the puffed spaceships travel parallel or anti-parallel to the puffer, as in this case they do not rake out any significant region of the Life plane (and, in contrast to true rakes, these puffers cannot travel in a stream, and so could never be produced by a gun).
Although the first rakes (circa 1971) were c/2, rakes of other velocities have since been built. Dean Hickerson's construction of Corderships in 1991 made it easy for c/12 diagonal rakes to be built, although no one actually did this until 1998, by which time David Bell had constructed c/3 and c/5 rakes (May 1996 and September 1997, respectively). Jason Summers constructed a 2c/5 rake in June 2000 (building on work by Paul Tooke and David Bell) and a c/4 orthogonal rake in October 2000 (based largely on reactions found by David Bell).
The smallest possible period for a rake is probably 7, as this could be achieved by a 3c/7 orthogonal backwards glider puffer. The smallest period attained to date is 8 (Jason Summers' backrake, March 2001).
Found by Dave Buckingham, 1972.
Found by Dean Hickerson in January 2016 and named by Jeremy Tan.
= bun. This name is due to the fact that the pattern is a single-cell modification of a beehive.
The collection of cells that are alive during some part of a given active reaction. This term is used for Herschel circuits and other stable circuitry, whereas construction envelope is specific to recipes in self-constructing circuitry.
There are some subtleties at the edges of the envelope. Specifically, two reactions that have the exact same set of cells defining their envelopes may have different behavior when placed next to a single-cell protrusion like the tail of an eater1, or one side of a tub. The difference depends on whether two orthogonally adjacent cells at the edge of the envelope are ever simultaneously alive, within the protruding cell's zone of influence.
A reaction performed by a convoy of spaceships (or other moving objects) which converts a common stationary object into a glider without harming the convoy. This provides one way for signals that have been frozen in place by some previous reaction to be released for use.
Simple reactions using period 4 c/2 spaceships have been found for reanimating a block, boat, beehive, ship, loaf, bi-block, or toad. The most interesting of these is for a beehive since it seems to require an unusual p4 spaceship:
Reanimation of a loaf is used many times in the Caterloopillar. It is also used in the Caterpillar as part of its catch and throw mechanism. Finally, reanimation can produce rakes from some puffers. See stop and restart for a similar idea that applies to Herschel conduits and other signal circuitry.
There are small objects which have no known reanimation reactions using c/2 ships other than the brute force method of hitting them with the output of rakes.
A very rare type of fuse whose output is identical to its input, possibly with some spatial and/or temporal offset. See lightspeed wire for an example. Reburnable fuses are used primarily in the construction of fixed-speed self-supporting macro-spaceships, where the speed of the fuse's burning reaction becomes the speed of the spaceship. Examples include the Caterpillar, Centipede, and waterbear.
See Herschel receiver.
The number of ticks that must elapse after a signal is sent through a conduit, before another signal can be safely sent on the same path. In general, a lower recovery time means a more useful conduit. For example, the Snark's very low recovery time allowed for the creation of oscillators with previously unknown periods, 43 and 53.
For the most part this is a synonym for repeat time. However, overclocking a complex circuit can often allow it to be used at a repeat time much lower than its safe recovery time.
The smallest known 180-degree reflector, discovered by Adam P. Goucher in 2009. It was the smallest and fastest stable reflector of any kind until the discovery of the Snark in 2013. The rectifier has the same output glider as the boojum reflector but a much shorter repeat time of only 106 ticks.
Another advantage of the rectifier is that the output glider is on a transparent lane, so it can be used in logic circuitry to merge two signal paths.
A toolkit developed by Alexey Nigin in July 2015, which enables the construction of patterns with population growth that asymptotically matches an infinite number of different superlinear functions. Toolkits enabling other, sublinear infinite series had been completed by Dean Hickerson and Gabriel Nivasch in 2006. See quadratic filter and exponential filter.
Sublinear functions are possible using the recursive-filter toolkit as well. It can be used to construct a glider-emitting pattern with a slowness rate S(t) = O(log***...*(t)), the nth-level iterated logarithm of t, which asymptotically dominates any primitive-recursive function f(t).
Any stable or oscillating pattern that can reflect some type of spaceship (usually a glider) without suffering permanent damage. A pattern that is damaged or destroyed during the reflection process is generally called a one-time turner instead.
The first known reflector was the pentadecathlon, which functions as a 180-degree glider reflector (see relay). Other examples include the buckaroo, the twin bees shuttle and some oscillators based on the traffic jam reaction. Glider guns can also be made into reflectors, although these are mostly rather large.
In September 1998 Noam Elkies found some fast small-period glider reflectors, with oscillators supplying the required domino sparks at different periods. A figure-8 produced a p8 bouncer, and a p6 pipsquirter produced an equivalent p6 bouncer. A more complicated construction allows a p5 bouncer (which, as had been anticipated, soon led to a true p55 Quetzal gun). And in August 1999 Elkies found a suitable sparker to produce a p7 bouncer, allowing the first p49 oscillator to be constructed.
These were all called simply "p5 reflector", "p6 reflector", etc., until 6 April 2016 when Tanner Jacobi discovered an equally small and simple reaction, the bumper, starting with a loaf as bait instead of a boat. This resulted in a series of periodic colour-preserving reflectors, whereas Elkies' bouncer reflectors are all colour-changing. A useful mnemonic is that "bouncer" contains a C and is colour-changing, whereas "bumper" contains a P and is colour-preserving.
Stable reflectors are special in that if they satisfy certain conditions they can be used to construct oscillators of all sufficiently large periods. It was known for some time that stable reflectors were possible (see universal constructor), but no one was able to construct an explicit example until Paul Callahan did so in October 1996.
Callahan's original reflector has a repeat time of 4840, soon improved to 1686, then 894, and then 850. In November 1996 Dean Hickerson found a variant in which this is reduced to 747. Dave Buckingham reduced it to 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. In November 1998 Callahan reduced this to 575 with a new initial reaction. A small modification by Silver a few days later brought this down to 497.
In April 2001 Dave Greene found a 180-degree stable reflector with a repeat time of only 202 (see boojum reflector). This reflector won bounties offered by Dieter Leithner and Alan Hensel. Half of the prize money was recycled into a new prize for a small 90-degree reflector, which in turn was won by Mike Playle's colour-preserving Snark reflector. The Snark is currently the smallest known stable reflector, with a recovery time of 43. Playle has offered a $100 prize for a colour-changing stable reflector contained within a 25 by 25 bounding box, with a recovery time of 50 generations or less.
As of June 2018, the following splitter is among the smallest known 90-degree colour-changing reflectors. The top output can be blocked off by an eater if needed. For small 180-degree colour-changing reflectors see rectifier, and also the sample pattern in splitter.
A pattern that rotates itself 90 or 180 degrees after some number of generations, with the additional constraint that multiple non-interacting copies of the pattern can be combined into a new oscillator with a period equal to the appropriate fraction of the component oscillators' period. The second constraint disqualifies small time-symmetric oscillators such as the blinker and monogram.
A working RRO might look something like a pi orbital or p256 gun loop containing one or more pis or Herschels in the same loop, but without any external stabilisation mechanism. Such patterns can be proven to exist (see universal constructor), but as of June 2018 none have been explicitly constructed in Life. There is no upper limit on multiplicity for a constructor-based RRO.
An object which converts input gliders aligned to some period to output gliders aligned to a different period. The most interesting case is a universal regulator, of which several have been constructed by Paul Chapman and others.
Any oscillator in which spaceships (typically gliders) travel in a loop. The simplest example is the p60 one shown below using two pentadecathlons. Pulling the pentadecathlons further apart allows any period of the form 60+120n to be achieved. This is the simplest proof of the existence of oscillators of arbitrarily large period.
Any oscillator or spaceship.
The minimum number of generations that is possible between the arrival of one object and the arrival of the next. This term is used for things such as reflectors or conduits where the signal objects (gliders or Herschels, for example) will interact fatally with each other if they are too close together, or one will interact fatally with a disturbance caused by the other. For example, the repeat time of Dave Buckingham's 59-step B-heptomino to Herschel conduit (shown under conduit) is 58.
The following reaction that shifts the phase and path of a pair of gliders. There is another form of this reaction, glider-block cycle, that reflects the gliders 180 degrees.
A finite pattern which repeatedly creates copies of itself. Such objects are known to exist (see universal constructor), but no concrete example is known. The linear propagator may be considered to be the first example of a replicator built in Life, but this is debatable as each of its copies replicates itself only once, allowing no possibility of superlinear growth.
A storage mechanism for data feeding a universal constructor designed by Adam P. Goucher in 2018. A very large integer can be encoded in the position of a very faraway object. If the distance to that object is measured using circuitry designed to be as simple as possible, a complete decoder and universal constructor can be created by colliding a small number of gliders - no more than 329 according to a June 2018 glider synthesis, and exactly 43 according to a July 1 redesign by Chris Cain using eight far-distant GPSEs and, amazingly, no stationary circuitry except for a single catalyst block. Some intermediate designs with 50+ gliders need no stationary circuitry at all.
With the correct placement of the faraway object, the complete pattern is theoretically capable of building any glider-constructible object. This means that 43 is the maximum number of gliders required to build any constructible object, no matter what size. However, it is not possible to determine in practice what the locations of these 43 gliders should be, even for a relatively simple construction.
A fuse that produces some initial debris, but then burns cleanly. The following is a simple example.
A converter with several known forms, many of which found by Dave Buckingham in 1972 and in the early 1980s. It accepts an R-pentomino as input and produces an output B-heptomino 28 ticks later. Of nine major variants known as of July 2018, four versions are shown below. For each version, the R-pentomino inputs are shown near the left and right edges, along with the B-heptomino output locations near the center.
The version in the southeast is used in Paul Callahan's Herschel receiver. The one in the northwest is part of L156, but can be replaced by the variant in the northeast which produces a forward glider output.
Stephen Silver's alternate completion of Paul Callahan's Herschel receiver. As of June 2018 there are four known variants. The original version consists of a single loaf. A ghost Herschel marks the output location.
A period 16 oscillator found by Rich Holmes in July 2016, using apgsearch. For its use as a filter see for example p48 gun.
The following muttering moat found by Dean Hickerson in September 1992.
Run-length encoded. Run-length encoding is a simple (but not very efficient) method of file compression. In Life the term refers to a specific ASCII encoding used for patterns in Conway's Life and other similar cellular automata. This encoding was introduced by Dave Buckingham and is now the usual means of exchanging relatively small patterns by email or in online forum discussions.
As an example of the rle format, here is a representation of the Gosper glider gun. The "run lengths" are the numbers, b's are dead cells, o's are live cells, and dollar signs signal new lines:
x = 36, y = 9, rule = B3/S23 24bo$22bobo$12boo6boo12boo$11bo3bo4boo12boo$oo8bo 5bo3boo$oo8bo3boboo4bobo$10bo5bo7bo$11bo3bo$12boo!
Over the years RLE format has been extended to handle patterns with multiple states, neighborhoods, rules, and universe sizes. A completely different encoding, macrocell format, is used for repetitive patterns that may have very large populations.
A small active reaction, so named because it is a single-cell modification of a mango, but now more commonly known as dove.
The following edge shooter converter, accepting an input R-pentomino and producing a glider heading northeast (if the R-pentomino is in standard orientation).
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Dean Hickerson's term for an eater which remains intact throughout the eating process. The snake in Dave Buckingham's 59-step B-to-Herschel conduit (shown under conduit) is an example. Other still lifes that sometimes act as rocks include the tub, the hook with tail, the eater1 (eating with its tail) and the hat (in Heinrich Koenig's stabilization of the twin bees shuttle).
Found by Robert Wainwright in 1972. See also multiple roteightors.
The cells of an oscillator that change state. Compare stator. It is easy to see that any rotor cell must be adjacent to another rotor cell.
This is by far the most active polyomino with less than six cells: all the others stabilize in at most 10 generations, but the R-pentomino does not do so until generation 1103, by which time it has a population of 116, including six gliders.
Wolfram's rule 22 is the 2-state 1-D cellular automaton in which a cell is ON in the next generation if and only if exactly one of its three neighbours is ON in the current generation (a cell being counted as a neighbour of itself). This is the behaviour of Life on a cylinder of width 1.
A pattern constructed by Dean Hickerson in April 2005 that produces a stream of LWSS with gaps in it, such that the number of LWSS between successive gaps follows the "ruler function" (sequence A001511 in The On-Line Encyclopedia of Integer Sequences).
Any oscillator in which the rotor is connected and contained in a strip of width 2. The following p3 example is by Dean Hickerson, November 1994.
A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in May 1997. It is made up of two elementary conduits, HR143B + BFx59H. After 202 ticks, it produces an inverted Herschel turned 90 degrees clockwise at (7, 32) relative to the input. Its recovery time is 201 ticks. A ghost Herschel in the pattern below marks the output location:
A boat hassled by a Kok's galaxy, a figure-8 and two eater3s. Found by Robert Wainwright in June 1984.
A collection of spaceships, usually gliders, all travelling in the same direction. Any valid glider construction recipe can be partitioned into no more than four salvos. Compare flotilla. In contrast with a convoy, the spaceships in a salvo are usually consumed by the reactions that they cause. Simple examples include block pusher and block pull.
Salvos may be slow or synchronized. The following partially synchronized three-glider salvo produces an LWSS from a block.
Any finite pattern whose population grows without bound but does not tend to infinity. (In other words, the population reaches new heights infinitely often, but also infinitely often returns to some fixed value.) Conway's preferred plural is "sawteeth".
The first sawtooth was constructed by Dean Hickerson in April 1991. The current smallest known sawtooth was found by a conwaylife.com forum user with the online handle 'thunk'. It has a bounding box of 74×60, and is the smallest known sawtooth in terms of its minimum repeating population of 177 cells. The following variant has a higher repeating population of 194 and an optimized bounding box of 62×56:
This spaceship, found by Paul Schick in 1972, produces a large spark (the 15 live cells at the rear in the phase shown below) which can be perturbed by other c/2 spaceships to form a variety of puffers. See blinker ship for an example perturbation of the spark. The diagram below shows the smallest form of the Schick engine, using two LWSS. It is also possible to use two MWSSes or two HWSSes, or even an LWSS and an HWSS.
Found in 1971.
The first diagonal c/6 spaceship, found by Nicolay Beluchenko in September 2005.
A computer program or script that automates the search for Life objects having certain desired properties. These are used because the difficulty of finding previously unknown Life objects now commonly exceeds the patience, speed, and accuracy of humans. Various types of search programs are used for finding objects such as spaceships, oscillators, drifters, catalysts, soups, Gardens of Eden, and slow salvos.
Some search programs generate partial results as they are running, so even if they don't complete successfully, something of use might still be salvaged from the run.
Example search programs are dr, lifesrc, gfind, and Bellman.
There are other types of programs which don't perform searches as such, but instead perform large constructions. These are used to correctly complete very complicated objects such as the Caterpillar, Gemini, Caterloopillar, and universal constructor-based spaceships such as the Demonoids and Orthogonoids.
The second glider domain of an edge shooter is the set of spacetime offsets, relative to the glider stream emitted by the edge shooter, where a second independent glider stream may be present without interfering with the edge shooter. This is useful to know, because edge shooters are often used to generate glider streams very close to other glider streams, to make for example a spaceship gun or converter.
The glider produced at T=72 during the evolution of a Herschel. This is the common edge-shooting glider output used in the NW31 converter and several other converter variants.
A constellation of still lifes and/or oscillators, which can be converted into another Life object when it is struck by one or more gliders. Usually the resulting object is a rare still life or spaceship, more complex than the original constellation. Spartan single-glider (1G) seeds are more commonly seen than multi-glider seeds, because a Spartan 1G seed can be readily constructed and triggered using a slow salvo. See also freeze-dried. For example, the following is a 14sL 1G seed for a c/7 loafer spaceship.
An interactive search application written by Paul Chapman in 2013. Its primary purpose was to assist in the design of self-destruct circuits in self-constructing circuitry. It has also regularly been helpful in completing glider syntheses, and was used to find the 31c/240 base reaction for the shield bug and Centipede spaceships.
A type of pattern, generally a macro-spaceship, that contains encoded construction information about itself, and makes a complete copy of itself using those instructions. The Gemini, linear propagator, spiral growth patterns, Demonoids and Orthogonoid are examples of self-constructing patterns. Self-constructing spaceships often have trivially adjustable speeds. In many cases, the direction of travel can also be altered, less easily, by changing the encoded construction recipe. Compare self-supporting, elementary.
A type of pattern, specifically a macro-spaceship, that constructs signals or tracks or other scaffolding to assist its movement, but does not contain complete information about its own structure. Examples include the Caterpillar, Centipede, half-baked knightship, waterbear, and the Caterloopillars. Caterpillar has been used as a general term for self-supporting spaceships, but it is not very appropriate for the HBKs.
In general a self-supporting pattern cannot be trivially adjusted to alter its speed or direction. The variable speeds of the HBKs and the Caterloopillars are exceptions, but their direction of travel is fixed, and a specific Caterloopillar can't be made to change its speed without completely rebuilding it. Compare self-constructing, elementary.
Either of two semi-Snark variants discovered by Tanner Jacobi in November 2017. The name is due to the initial converter, which produces a century output for every two input gliders. The minimum safe repeat time is 43 ticks for the smaller initial catalyst shown in CC semi-cenark and CP semi-cenark, or 42 ticks with the slightly larger catalyst variant shown below. There is also overclocking possible at period 36, 38, or 39. The reset glider can be followed immediately by a new trigger glider, as shown below, so the minimum repeat time for an intermittent stream of gliders is only 50 ticks.
Any small stable signal conduit that produces one output glider for every two input gliders, with a 90 degree reflection. These can act as period-doublers for any glider stream whose period is at least equal to their repeat time, and so adding one of these to a single glider gun often results in a pattern much smaller than the older technology of crossing the output of two guns.
The available semi-Snarks differ in their complexity, size, repeat time, and the colour of their output gliders. The CC semi-Snark was the first one found, and the term "semi-Snark" is often used specifically for this object. The "CC" prefix stands for colour-changing, by contrast with the more recently discovered colour-preserving CP semi-Snark.
There are also CC and CP variants of a semi-Snark based on a two-glider to century converter discovered by Tanner Jacobi in November 2017. These semi-cenarks are the fastest semi-Snarks known as of July 2018, with a repeat time as low as 50 ticks, or a periodic input rate as low as 36 ticks.
Halfway between a hat and a twinhat.
Abbreviation for stable glider reflector. This term is no longer in use.
The first 31c/240 macro-spaceship, constructed by Dave Greene on September 9, 2014.
The term is also used as a synonym of spaceship.
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A ship can be used as a catalyst in some situations. For example, it can suppress two of the blinkers from an evolving traffic light:
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Found by Bill Gosper in August 1994. See also bottle.
= ship-tie
The name is by analogy with boat-tie.
Found by Dean Hickerson, August 1989. See also bent keys and odd keys.
A gun that fires a salvo of multiple spaceships, almost always gliders, on parallel lanes. Two to four shotguns are often combined to turn a glider synthesis into a gun or factory for that synthesis.
The fixed upper end of a construction arm, generally consisting of one or more glider guns or edge shooters aimed at an elbow object.
Any oscillator which consists of an active region moving back and forth between stabilizing objects. The most well-known examples are the queen bee shuttle (which has often been called simply "the shuttle") and the twin bees shuttle. See also p54 shuttle, p130 shuttle and Eureka. Another example is the p72 R-pentomino shuttle that forms part of the pattern given under factory.
A term used in naming certain still lifes (and the stator part of certain oscillators). It indicates that the object consists of two smaller objects sharing two or more cells. See snake siamese snake and loaf siamese barge for examples.
Half a sidewalk. In itself this is unstable and requires an induction coil.
A small tagalong for an HWSS that was found by Hartmut Holzwart in 1992. The resulting spaceship (shown below) has a phase with only 24 cells, making it in this respect the smallest known spaceship other than the standard spaceships and some trivial two-spaceship flotillas derived from them. Note also that an HWSS can support two sidecars at once.
A Spartan eater found by Chris Cain in May 2015 with functionality similar to the eater5, as shown below. It has one lane less diagonal clearance on the high-clearance side than other eater5 variants, due to the presence of the boat. A good use of the sidesnagger can be seen in p130 shuttle. See also highway robber.
Found by Dave Buckingham in 1973. Compare sombreros.
Movement of information through the Life universe. Signals can be carried by spaceships, fuses, drifters, or conduits. Spaceships can only transfer a signal at the speed of the spaceship, while fuses can transfer a signal at speeds up to the speed of light.
In practice, many signals are encoded as the presence or absence of a glider or other spaceship at a particular point at a particular time. Such signals can be combined by the collision of gliders to form logic operations such as AND, OR, and NOT gates. Signals can be duplicated using glider duplicators or other fanout devices, and can be used up by causing perturbations on other parts of the Life object.
Signals are used in Herschel conduit circuitry, universal constructors, macro-spaceships, and other computational patterns such as the pi calculator and Osqrtlogt patterns.
A conduit with signal output 90 degrees from its input. This term is commonly used only for signal wires, particularly 2c/3 signals. A Snark could reasonably be called a "glider elbow", but glider reflector is the standard term. A signal elbow with a recovery time less than 20 ticks would enable a trivial proof that Conway's Life is omniperiodic.
A near miss is the following elbow-like converter found by Dean Hickerson. It successfully turns a 2c/3 signal by 90 degrees, but unfortunately changes it to a double-length signal in the process. This means that further copies of the converter can not be appended (e.g., to make a closed loop).
Relatively small composite MWSS elbows can now be constructed, using Tanner Jacobi's 2015 discovery of a small H-to-MWSS component. For example, the Orthogonoid includes a constructor/reflector that reflects an MWSS stream by 180 degrees, but it can be trivially reconfigured to make a 90-degree MWSS elbow.
A variant of the Silver reflector made by substituting an Fx119 conduit for the final NW31, allowing a Herschel output as well as the beehive-annihilating reset glider. It is still Spartan, and as long as the Fx119 is followed by a dependent conduit, it retains the faster 497-tick recovery time.
A stable glider reflector found by Stephen Silver in November 1998, by substituting an NW31 converter for the second Fx77 conduit in the Callahan G-to-H found a few days previous. The repeat time is 497 ticks:
The following oscillator found by Stephen Silver in February 2000:
As this has no spark, it appears useless. Nonetheless, in March 2000, David Eppstein found a way to use it to reduce the size of Noam Elkies' p5 reflector.
A Herschel-based glider gun discovered by Michael Simkin in April 2015. It consists of a Herschel running through two B60 conduits. In terms of its 36-cell minimum population, it is one of the smallest known guns, sharing the record with the Gosper glider gun. In the double-barreled form, as well as the pseudo-period, snake-stabilized form shown below, it is the absolute record holder.
A type of universal constructor using just one construction arm and slow salvo techniques to construct, usually, Spartan or near-Spartan circuitry. Compare two-arm.
A type of universal constructor discovered and developed by Simon Ekström and others starting in December 2015. The initial elbow operation toolkit was near-minimal, with just one push, one pull, and one output glider of each colour (see colour of a glider). Later searches produced a much larger and more efficient library.
Single-channel recipes consist of a stream of gliders on a single lane and aimed at a construction elbow, usually separated from each other by at least 90 ticks. In spite of these strict limitations, single-channel recipes can be made to do surprising things. For example, it is possible to build a Snark directly on the construction lane of an active construction arm, starting from a single elbow block. This can allow the arm to reach efficiently around complex obstructions by bending itself through multiple lossless elbows. Known recipes can also remove an elbow when it is no longer needed, by controlled demolition of the Snark.
As of June 2018, almost all single-channel recipes are made up of singletons and synchronized pairs of gliders, but no synchronized triplets or larger groups. This is not an inherent limitation of single-channel construction, but rather a limitation in the search program used to find currently known single-channel toolkits.
A useful byproduct of this limitation is that single-channel recipes can be trivially adjusted to allow them to safely cross perpendicular data streams, including other single-channel recipes (or earlier parts of the same recipe). To avoid collisions with a crossing stream, each singleton glider or glider pair can safely be delayed by any even number of ticks, or technically by any multiple of the period of the current intermediate target. The final result of the construction will not be affected.
See Demonoid.
In single-channel recipes, a glider that is not synchronized with a neighboring glider in its stream. Compare glider pair.
Found by Robert Wainwright, July 1972.
= canoe
The first elementary knightship in Conway's Game of Life, found by Adam P. Goucher on March 6, 2018, based on a partial by Tomas Rokicki.
This is a compact form of loading dock.
Found by Robert Wainwright, October 1978.
Found by Robert Wainwright, August 1989.
Abbreviation for still life, used most often in rough measurements of the complexity of a Spartan constellation.
A gun which fires sideways from an extending arm. The arm consists of streams of spaceships which are pushing a pattern away from the body of the gun and releasing an output spaceship every time they do so. Each output spaceship therefore travels along a different path.
Dieter Leithner constructed the first slide gun in July 1994 (although he used the term "side shooting gun"). The following pattern shows the key reaction of this slide gun. The three gliders shown will push the block one cell diagonally, thereby extending the length of the arm by one cell, and at the same time they release an output glider sideways. (In 1999, Jason Summers constructed slide guns using other reactions.)
A memory register whose value is stored as the position of a block. The block can be moved by means of glider collisions. See block pusher for an example.
In Conway's original formulation (as part of his proof of the existence of a universal computer in Life) two gliders were used to pull the block inwards by three diagonal spaces, as shown below, and thirty gliders were used to push it out by the same amount.
Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out the same distance using 3 gliders. In order for the memory to be of any use there also has to be a way to read the value held. It suffices to be able to check whether the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did).
Dean Hickerson's sliding block memory is used in Paul Chapman's URM, and the key salvos from it are used in several other complex constructions, such as David Bell's Collatz 5N+1 simulator and Adam P. Goucher's pi calculator and Spartan universal computer-constructor.
A search program published by Adam P. Goucher in May 2017. It accepts as input a constellation of sufficiently widely separated still lifes, and produces a glider stream that will perform a complete slow glider construction of that constellation, starting from a single block.
One of slmake's primary uses is to make self-constructing patterns much easier to design and build. It is capable of finding recipes not only for Spartan stable circuitry, but also for other useful non-Spartan circuits such as Snarks, syringes, and H-to-MWSS converters, provided that they are separated from other nearby objects by a sufficient amount of empty space.
A movable construction elbow that is controlled by a slow salvo, which most likely comes from a previous elbow in a multi-elbow construction arm. Unlike a standard elbow which is generally fixed on a single construction lane or at least within a narrow range, a slow elbow can move freely in two dimensions as long as there is room for it. Each slow elbow added to a construction arm results in an exponential increase in the cost (in gliders) of the final construction. Compare lossless elbow.
Construction an object by a "slow salvo" of gliders all coming from the same direction, in such a way that timing of the gliders does not matter as long as they are not too close behind one another. This type of construction requires an initial seed object, such as a block, which is modified by each glider in turn until the desired object is produced.
In May 1997, Nick Gotts produced a slow glider construction of a block-laying switch engine from a block, using a slow salvo of 53 gliders. Constructions like this are important in the study of sparse Life, as they will occur naturally as gliders created in the first few generations collide with blonks and other debris.
Slow glider constructions are also useful in some designs for universal constructors. However, in this case the above definition is usually too restrictive, and it is desirable to allow constructions in which some gliders in the salvo are required to have a particular timing modulo 2 (a "p2 slow salvo"). This gives much greater flexibility, as blinkers can now be freely used in the intermediate construction steps. The Snarkmaker is a very large p2 slow salvo. A much smaller example is the following edgy construction of an eater1 starting from a block.
Adam P. Goucher's slmake search program, made available in May 2017, makes it much easier to find a slow glider construction for a wide variety of stable circuitry.
= LWSS
A 20-cell still life, but technically not actually a lake because it is not constructed entirely out of dominoes.
Found by Achim Flammenkamp in July 1994 and named by Alan Hensel.
See breeder.
Debris that is fairly long-lived but eventually dies completely. Basically, a large spark. This term is used especially when talking about the output from a smoking ship. Some Herschel conduits such as Fx119 also create large amounts of smoke.
A spaceship which produces smoke. If the smoke extends past the edge of the rest of the spaceship, then it can be used to perturb other objects as the spaceship passes by. Running gliders into the smoke is often a good way to turn or duplicate them, or convert them into other objects. Sometimes the smoke from a smoking ship may itself be perturbed by accompanying spaceships in order to form a puffer. A simple example of a smoking ship is the Schick engine.
Found by Mark Niemiec in 1972. This is a pentadecathlon with stabilizers which force it into a lower period.
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The first known c/5 spaceship, discovered by Tim Coe in January 1996. For some time it was the slowest known orthogonal spaceship.
An alternative name for a boat-bit. Not a very sensible name, because various other things can be used instead of a snake. A snake, or alternatively an aircraft carrier, is the smallest object that can consume a glider stream by effectively acting as an eater for every two incoming gliders. The one-cell reduction from the smallest real eater, the seven-cell eater1, has been important when trying to construct recent sawtooths where the population must be minimized.
Found by Robert Wainwright, May 1972.
This term has been used for two different oscillators: the p2 snake pit (essentially the same as fore and back)
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A small stable 90-degree glider reflector with a repeat time of 43 ticks, discovered by Mike Playle on 25 April 2013 using a search utility he wrote called Bellman. Compare boojum reflector. Four common Snark variants are shown below: Playle's original at the top, and variants by Heinrich Koenig, Simon Ekström, and Shannon Omick to the left, bottom, and right, respectively. As of June 2018, only Playle's variant has a known slow glider construction recipe for all orientations.
A single-channel stream of gliders that, when aimed to collide with an elbow block in a specific location, will perform a slow glider construction of a Snark, directly on the same lane as the incoming gliders. This allows a construction arm to add one or more lossless elbows, so that it can bend around multiple corners without an exponential increase in construction cost.
The Snarkmaker recipe used in the first single-channel Demonoid, Orthogonoid, and spiral growth patterns contains 2,254 gliders. This could be considerably reduced with a customized search program.
Found by Dave Buckingham in 1972. If the two halves are moved three spaces closer to one another then the period drops to 4, and the result is just a less compact form of Achim's p4. Compare also siesta.
A random initial pattern, either contained within a small area, or alternatively filling the whole Life universe.
Finite soups probably have behaviors very different than infinite soups, but this is obviously unknown. Infinite soups may remain chaotic indefinitely since any reaction, no matter how rare, is bound to happen somewhere.
Soups can have an average density, with results varying based on that. See sparse Life for a discussion of what can happen at a low density.
Finite soups for sizes such as 16×16 (asymmetric) have been examined by the billions by scripts such as apgsearch to find interesting results. Many new oscillators and synthesis recipes have been discovered, as well as previously known rare patterns such as stabilized switch engines. In addition, soups are used to generate statistical census data, and to decide whether specific objects can be considered natural.
Soups can be fully random, or they can be forced to be symmetric. The results for these two types of soups can differ since symmetric soups tend to create large symmetrical objects at a much higher rate. Shown below is an unusual mirror-symmetric soup that produces a pufferfish and nothing else.
A part of a spaceship or oscillator which looks like a random mix of ON and OFF cells. It is usually very difficult to find a glider synthesis for an object that consists wholly or partly of space dust. As examples, the 295P5H1V1, fly, and seal spaceships contain large amounts of space dust.
Any pattern that grows at a quadratic rate by filling space with an agar. The first example was found in September 1993 by Hartmut Holzwart, following a suggestion by Alan Hensel. The diagram below shows a smaller spacefiller found by Tim Coe. See also Max. Spacefillers can be considered as breeders (more precisely, MMS breeders), but they are very different from ordinary breeders. The word "spacefiller" was suggested by Harold McIntosh and soon became the accepted term.
Any pattern that expands indefinitely to affect every cell in the Life plane, but leaves an expanding region of vacuum at its center. Compare spacefiller; see also antstretcher. The first nonfiller was discovered by Jason Summers on 14 April 1999:
The following p20 forwards glider rake, which was the first known rake. It consists of an ecologist with a LWSS added to turn the dying debris into gliders.
Any finite pattern that reappears (without additions or losses) after a number of generations and displaced by a non-zero amount. By far the most natural spaceships are the glider, LWSS, MWSS and HWSS, followed by the Coe ship which has also evolved multiple times from random asymmetric soup starting conditions. See also the entries on individual spaceship speeds: c/2 spaceship, c/3 spaceship, c/4 spaceship, c/5 spaceship, c/6 spaceship, c/7 spaceship, c/10 spaceship, c/12 spaceship, 2c/5 spaceship, 2c/7 spaceship, 3c/7 spaceship, (2,1)c/6 spaceship, and 17c/45 spaceship.
It is known that there exist spaceships travelling in all rational directions and at arbitrarily slow speeds (see universal constructor). Before 1989, however, the only known examples travelled at c/4 diagonally (gliders) or c/2 orthogonally (everything else).
In 1989 Dean Hickerson started to use automated searches to look for new elementary spaceships, and had considerable success. Other people have continued these searches using tools such as lifesrc and gfind, and as a result we now have a great variety of elementary spaceships travelling at sixteen different velocities. The following table details the discovery of elementary spaceships with new velocities as of July 2018.
----------------------------------------------------------------- Speed Direction First Discovery Discoverer Date ----------------------------------------------------------------- c/4 diagonal glider Richard Guy 1970 c/2 orthogonal LWSS John Conway 1970 c/3 orthogonal 25P3H1V0.1 Dean Hickerson Aug 1989 c/4 orthogonal 119P4H1V0 Dean Hickerson Dec 1989 c/12 diagonal Cordership Dean Hickerson Apr 1991 2c/5 orthogonal 44P5H2V0 Dean Hickerson Jul 1991 c/5 orthogonal snail Tim Coe Jan 1996 2c/7 orthogonal weekender David Eppstein Jan 2000 c/6 orthogonal dragon Paul Tooke Apr 2000 c/5 diagonal 295P5H1V1 Jason Summers Nov 2000 c/6 diagonal seal Nicolay Beluchenko Sep 2005 c/7 diagonal lobster Matthias Merzenich Aug 2011 c/7 orthogonal loafer Josh Ball Feb 2013 c/10 orthogonal copperhead zdr Mar 2016 3c/7 orthogonal spaghetti monster Tim Coe Jun 2016 (2,1)c/7 oblique Sir Robin Adam P. Goucher Mar 2018 -----------------------------------------------------------------
Several infinite families of adjustable-velocity macro-spaceships have also been constructed, of which the first was Gabriel Nivasch's Caterpillar from December 2004. The macro-spaceship with the widest range of possible speeds is Michael Simkin's Caterloopillar from April 2016; in theory it supports any rational orthogonal speed strictly less than c<4. A somewhat similar design supporting any rational speed strictly less than c/2 has been shown to be feasible, but as of July 2018 no explicit examples have been constructed.
A period p spaceship that displaces itself (m,n) during its period, where m>=n, is said to be of type (m,n)/p. It was proved by Conway in 1970 that p>=2m+2n. (This follows immediately from the easily-proved fact that a pattern cannot advance diagonally at a rate greater than one half diagonal step every other generation.)
A series of articles posted by David Bell to the newsgroup comp.theory.cell-automata during the period August-October 1992 that described many of the new spaceships found by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an addendum covering more recent developments in 1996.
The first 3c/7 spaceship, found by Tim Coe in June 2016. The spaceship travels orthogonally, has a minimum of 702 live cells and fits in a 27×137 bounding box.
A pattern that dies. The term is typically used to describe a collection of cells periodically thrown off by an oscillator or spaceship, but other dying patterns, particularly those consisting or only one or two cells (such as produced by certain glider collisions, for example), are also described as sparks. For examples of small sparks see unix and HWSS. Examples of much larger sparks are seen in Schick engine and twin bees shuttle spark.
Found in 1971.
An oscillator or spaceship that produces sparks. These can be used to perturb other patterns without being themselves affected.
One of two eaters found in April 1997 and November 1998 by Dean Hickerson using his dr search program, shown below to the left and right respectively. These both absorb gliders as a standard eater does, but also produce separated single-bit sparks at the upper right, which can be used to delete antiparallel gliders with different phases as shown.
The separation of the spark also allows this reaction to perform other perturbations "around the corner" of some objects. For example, it was used by Jason Summers in 2004 to cap the ends of a row of ten AK47 reactions to form a much smaller period 94 glider gun than the original one. (This is now made obsolete by the AK94 gun.)
A certain c/4 tagalong, shown here attached to the back of a spaceship.
This refers to the study of the evolution of a Life universe which starts off as a random soup of extremely low density. Such a universe is dominated at an early stage by blocks and blinkers (often referred to collectively as blonks) in a ratio of about 2:1. Much later it will be dominated by simple infinite growth patterns (presumably mostly switch engines). The long-term fate of a sparse Life universe is less certain. It may possibly become dominated by self-reproducing patterns (see universal constructor), but it is not at all clear that there is any mechanism for these to deal with all the junk produced by switch engines.
A pattern composed of subunits that can be easily constructed in any orientation, usually with a slow salvo. Generally this means that the pattern is a constellation of Spartan still lifes: block, tub, boat, hive, ship, loaf, eater1, or pond. Other small objects may sometimes be counted as Spartan, including period-2 oscillators - mainly blinkers, but also beacons or toads, which may occur as intermediate targets in slow salvo recipes. Most self-constructing patterns are Spartan or mostly Spartan, to simplify the process of self-construction.
Any mechanism which allows a signal (indicated by the presence or absence of a spaceship) to move faster than the spaceship could travel through empty space. The original speed booster is based on p30 technology, and is shown below:
The fastest speed boosters are the telegraph and p1 telegraph, which can transfer a orthogonal signal at the speed of light, although their bit rate is rather slow.
Diagonal speed boosters have also been built using 2c/3 wires or other stable components. See stable pseudo-Heisenburp.
The star gate seems like it can transfer a signal faster than the speed of light. The illusion is explained in Fast Forward Force Field.
The greatest speed at which any effect can propagate; in Life, a speed of one cell per generation. Usually denoted c.
Conway's name for the following pentomino, which rapidly dies.
This is the smallest known c/5 spaceship, and was found by David Bell in April 1997. Its side sparks have proved very useful in constructing c/5 puffers, including rakes. See also PPS.
Found by Robert Wainwright in 1971.
A self-constructing pattern built by Dave Greene in August 2014 that uses four universal constructors (UCs) arranged in a diamond to build four more UCs in a slightly larger diamond. This was the first B3/S23 pattern that exhibited spiral growth. Much smaller versions have now been constructed using the single-channel construction toolkit.
A signal converter that accepts a single input signal and produces two or more output signals, usually of the same type as the input. An older term for this is fanout, or "fanout device".
A sub-category is the one-time splitter, which is not technically a converter because it can only be used once. One-time splitters are usually small constellations that produce two or more clean gliders when struck by a single glider. In other words, they are multi-glider seeds. These are important for constructing self-destruct circuitry in self-constructing spaceships.
The following combination, a syringe attached to an SE7T14 converter combined with an NW31 converter, is one of the smallest known glider splitters as of July 2018. Another small splitter with a 90-degree colour-changing output is shown under reflector.
The symmetric PPS. The original PPS found by David Bell in May 1998. Compare APPS.
Any glider-emitting pattern which emits its nth glider at a time asymptotically proportional to n2. The first examples were constructed by Dean Hickerson around 1991. See also quadratic filter, exponential filter, recursive filter.
The p2 agar formed by tiling the plane with the following pattern. Found by Don Woods in 1971.
= big S
A single switch engine which survives indefinitely by interacting with the appropriate exhaust such that it prevents the engine from ever being destroyed.
The only known types of stabilized switch engines were found by Charles Corderman soon after he discovered the switch engine itself. There is a p288 block-laying type (the more common of the two) and the p384 glider-producing type. These two puffers are the most natural infinite growth patterns in Life. As of June 2018 they are the basis for every infinite growth pattern ever seen to occur from a random asymmetric soup, even after trillions of census results by apgsearch and similar projects.
Patterns giving rise to block-laying switch engines can be seen under infinite growth, and one giving rise to a glider-producing switch engine is shown under time bomb.
Here is the block-laying type showing its distinctive zig-zag trail of blocks.
A pattern is said to be stable if it is a parent of itself. Stable objects are oscillators with period 1 (p1), and are generally called still lifes.
A multi-stage converter constructed by Dave Greene in January 2007, using a complex recipe found by Noam Elkies to insert a signal into a 2c/3 wire. The wire's high transmission speed allows a signal from a highway robber to catch up to a salvo of gliders. Ultimately the mechanism restores the key glider, which was destroyed by the highway robber in the first stage of the converter, to its exact original position in the salvo.
Much smaller stable pseudo-Heisenburp devices have since been designed that use simple 0-degree glider seed constellations instead of a 2c/3 wire.
These patterns are labeled "pseudo-Heisenburp", because a true Heisenburp device does not even temporarily damage or affect a passing glider, yet can still produce an output signal in response. However, it is impossible to construct a stable device that can accomplish this for gliders. True stable Heisenburp devices are possible with many other types of spaceships, but not with gliders which have no usable side sparks to initiate an output signal.
A type of signal-processing circuit where the initial reaction between catalysts an incoming signal results in an imperfect recovery. A catalyst is damaged, destroyed completely as in a bait reaction, or one or more objects are left behind that must be cleaned up before the circuit can be reused. In any of these three cases, output signals from the circuit must be used to complete the cleanup. In theory the cleanup process might itself be dirty, requiring additional cleanup stages. In rare cases this might theoretically allow the construction of special-purpose circuits with a lower recovery time than would otherwise be possible, but in practice this kind of situation does not commonly arise.
An example is the record-breaking (at the time) 487-tick reflector constructed by Adam P. Goucher on 12 April 2009. 487 ticks was a slight improvement over the repeat time of the Silver reflector. The reflector featured a standard Callahan G-to-H, with cleanup by an internal dirty glider reflector found by Dieter Leithner many years before. This in turn was cleaned up by the usual ungainly Herschel plumbing attached to the G-to-H's output. The dirty glider reflector is not actually fully recovered before a second p487 signal enters the full reflector. However, it has been repaired by the time the internal reflector is actually needed again, so the cycle can be successfully repeated at p487 instead of p497.
The following predecessor of the blockade.
A collection of oscillators (or perhaps other Life objects) in a single diagram, displaying the exhibits much like stamps in a stamp album. The classic examples are by Dean Hickerson (see http://conwaylife.com/ref/DRH/stamps.html).
Many stamp collections contain "fonts" made of single cells (which cleanly die) to annotate the objects or to draw boxes around them. For example, here is a stamp collection which shows all the ways that two gliders can create a loaf or an eater:
Alternatively, stamp collections can use LifeHistory for their annotations, but this requires a more sophisticated Life program to handle. Numbers, or more rarely letters, are sometimes constructed from stable components such as blocks or snakes, but their readability is somewhat limited by placement constraints.
A glider, LWSS, MWSS or HWSS. These have all been known since 1970.
Found by Hartmut Holzwart, February 1993.
for transporting a LWSS faster than the speed of light. The key reaction is the Fast Forward Force Field.
The cells of an oscillator that are always on. Compare rotor. (The stator is sometimes taken to include also some of those cells which are always off.) The stator is divided into the bushing and the casing.
By analogy, the cells of an eater that remain on even when the eater is eating are considered to constitute the stator of the eater. This is not always well-defined, because an eater can have more than one eating action.
A statorless oscillator is one in which no cell is permanently on - that is, the stator is empty, or in other words the oscillator has the maximum possible volatility. See the volatility entry for examples of this type of oscillator at different periods. Statorless oscillators can be constructed for any sufficiently large period, using universal constructor technology.
Found by Josh Ball, June 2016. The first and only known statorless period 5 oscillator.
Another term for a generation or tick. This term is particularly used in describing conduits. For example, a 64-step conduit is one through which the active object takes 64 generations to pass.
Found by Robert Wainwright, September 1985. This is one of only three essentially different p3 oscillators with only three cells in the rotor. The others are 1-2-3 and cuphook.
Any stable pattern, usually assumed to be finite and nonempty. For the purposes of enumerating still lifes this definition is, however, unsatisfactory because, for example, any pair of blocks would count as a still life, and there would therefore be an infinite number of 8-bit still lifes.
For this reason a stricter definition is often used, counting a stable pattern as a strict still life only if its islands cannot be divided into two or more nonempty sets both of which are stable in their own right. If such a subdivision can be made, the pattern can be referred to as a constellation. If its cells form a single cluster it is also, more specifically, either a pseudo still life or a quasi still life.
In rare cases above a certain size threshold, a pattern may be divisible into three or four stable nonempty subsets but not into two. See the 32-bit triple pseudo (32 bits) and the 34-bit quad pseudo for examples.
All still lifes up to 18 bits have been shown to be glider constructible. It is an open question whether all still lifes can be incrementally constructed using glider collisions. For a subset of small still lifes that have been found to be especially useful in self-constructing circuitry, see also Spartan.
The smallest still life is the block. Arbitrarily large still lifes are easy to construct, for example by extending a canoe or barge. The maximum density of a large still life is 1/2, which can be achieved by an arbitrarily large patch of zebra stripes or chicken wire, among many other options. See density for more precise limits.
A tagalong which takes the form of a still life in at least one phase. An example is shown below.
A pattern by Dean Hickerson in which a period 46 shuttle converts a glider into a block on one oscillation, and then converts the block back into a glider on the next oscillation. The glider is reflected back onto its own path, but with a delay.
A type of signal circuit where an input signal is converted into a stationary object, which is then re-activated by a secondary input signal. This can be used either as a memory device storing one bit of information, or as a simple delay mechanism. In the following January 2016 example by Martin Grant, a ghost Herschel marks the output signal location, and a "ghost beehive" marks the location of the intermediate still life.
The catch and throw technology in a Caterpillar is a somewhat similar idea. See also stop and go and reanimation.
A line of identical objects (usually spaceships), each of which is moving in a direction parallel to the line, generally on the same lane. In many uses the stream is periodic. For example, the new gun produces a period 46 glider stream. The stream produced by a pseudo-random glider generator can have a very high period. Compare with wave. See also single-channel for a common use of non-periodic glider streams.
Any pattern that grows by stretching a wick or agar. See wickstretcher and spacefiller.
A still life that is either a single connected polyplet, or is arranged such that a stable smaller pattern cannot be formed by removing one or more of its islands. For example, beehive with tail is a strict still life because it is connected, and table on table is a strict still life because neither of the tables are stable by themselves. See also triple pseudo, quad pseudo.
Still lifes have been enumerated by Conway (4-7 bits), Robert Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham (14 bits), Mark Niemiec (15-24 bits), and Simon Ekström and Nathaniel Johnston (25-32 bits). The resulting figures are shown below; see also https://oeis.org/A019473. The most recent search by Nathaniel Johnston has also confirmed that the triple pseudo pattern found by Gabriel Nivasch is the only such still life with 32 bits or less. It is therefore included in the pseudo still life count and not in the table below.
-------------- Bits Number -------------- 4 2 5 1 6 5 7 4 8 9 9 10 10 25 11 46 12 121 13 240 14 619 15 1353 16 3286 17 7773 18 19044 19 45759 20 112243 21 273188 22 672172 23 1646147 24 4051711 25 9971377 26 24619307 27 60823008 28 150613157 29 373188952 30 926068847 31 2299616637 32 5716948683 --------------
As the number of bits increases, the strict still life count goes up exponentially by approximately O(2.46n). By comparison, the rate for pseudo still life}s is about O(2.56n) while for quasi still lifes it's around O(3.04n).
A term suggested by Noam Elkies in August 1998 for the proportion of cells involved in a period n oscillator which themselves oscillate with period n. For prime n this is the same as the ordinary volatility. Periods with known strictly-volatile oscillators include 1, 2, 3, 5, 6, 8, 13, 15, 22, 30, 33, and 177. Examples include figure-8, Kok's galaxy, smiley, and pentadecathlon. A composite example is the following p22, found by Nicolay Beluchenko on 4 March 2009:
A p4 sparker which produces a 1-cell spark that is separated from the rest of the oscillator by two clear rows of cells. The first superfountain was found by Noam Elkies in February 1998. In January 2006 Nicolay Beluchenko found the much smaller one shown below. See also fountain.
Growth faster than any rate proportional to T, where T is the number of ticks that a pattern has been run. This term usually applies to a pattern's population growth, rather than diametric growth or bounding-box growth. For example, breeders' and spacefillers' population asymptotically grows faster than any linear-growth pattern. It may also be used to describe the rate of increase in the number of subpatterns present in a pattern, such as when describing a replicator's rate of reproduction. Due to limits enforced by the speed of light, no pattern's population can grow at an asymptotic rate faster than quadratic growth. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
An infinite orthogonal row of cells stabilized on one side so that it moves at the speed of light, often leaving debris behind. The first examples were found in 1971 by Edward Fitzgerald and Robert Wainwright. Superstrings were studied extensively by Peter Rott during 1992-1994, and he found examples with many different periods. (But no odd periods. In August 1998 Stephen Silver proved that odd-period superstrings are impossible.)
Sometimes a finite section of a superstring can be made to run between two tracks ("waveguides"). This gives a fuse which can be made as wide as desired. The first example was found by Tony Smithurst and uses tubs. (This is shown below. The superstring itself is p4 with a repeating section of width 9 producing one blinker per period and was one of those discovered in 1971. With the track in place, however, the period is 8. This track can also be used with a number of other superstrings.) Shortly after seeing this example, in March 1997 Peter Rott found another superstring track consisting of boats. At present these are the only two waveguides known. Both are destroyed by the superstring as it moves along. It would be interesting to find one that remains intact.
See titanic toroidal traveler for another example of a superstring.
Those parts of an object which are only present in order to keep the rest of the object (such an engine or an edge spark) working correctly. These can be components of the object, or else accompanying objects used to perturb the object. In many cases there is a wide variation of support possible for an engine. The arms in many puffers are an example of support.
Found by Dave Buckingham, November 1972.
A Herschel-to-glider converter that produces a tandem glider useful in the tee reaction. It is classified as a "G3" converter because its two gliders are three lanes apart.
The simplest type of H-to-G converter, where the converter's effect is simply to suppress a Herschel cleanly after allowing its first natural glider to escape. The name should be read as "SW minus two", where -2 is a glider lane number. The complete designation is SW-2T21. See NW31T120 for a discussion of the standard naming conventions used for these converters.
An unlimited number of converters have the SW-2T21 classification. The variants most often used consist of just one or two small still life catalysts.
= SW-2
A diagonal spaceship producing some useful sparks. Found by Tim Coe in February 1996.
A signal-carrying circuit that can send output signals to two or more different locations, depending on the state of the mechanism. These may be toggle circuits, where the state of the switch changes after each use, or permanent switches that retain the same state through many uses until a change is made with a separate signal.
More generally, any circuit may be referred to as a switch, if it can alter its output based on stored information. For example, the following simple mechanism based on an eater2 was discovered by Emerson J. Perkins in 2007. It either reflects or absorbs an incoming signal, depending on the presence or absence of a nearby block. The block is removed if a reflection occurs.
The switching signal here is a glider produced by a high-clearance syringe variant found by Matthias Merzenich. The syringe is not technically part of the switch mechanism; any standard Herschel source can deliver the signal to the block factory (the two eater1s on the right side of the pattern). Alternate converter mechanisms could also be used to place the block.
An earlier example of the same type of one-time switch mechanism, also mediated by a block, can be found in the NW34T204 H-to-G. See also bistable switch for a very robust and versatile toggle switch with two input lanes and four possible outputs.
A gun that includes a mechanism to turn the output stream off and on with simple signals, often gliders. A small example is Dieter Leithner's switchable LWSS gun from July 8, 1995. The ON signal enters from the northeast, and the OFF signal from the northwest:
The following pattern discovered by Charles Corderman in 1971, which is a glide symmetric unstable puffer which moves diagonally at a speed of c/12 (8 cells every 96 generations).
.png)
The exhaust is dirty and unfortunately catches up and destroys the switch engine before it runs 13 full periods. Corderman found several ways to stabilize the switch engine to produce puffers, using either one or two switch engines in tandem. See stabilized switch engine and ark.
No spaceships were able to be made from switch engines until Dean Hickerson found the first one in April 1991 (see Cordership). Switch engine technology is now well-advanced, producing many c/12 diagonal spaceships, puffers, and rakes of many periods.
Small polyominoes exist whose evolution results in a switch engine. See nonomino switch engine predecessor.
Several three-glider collisions produce dirty reactions that produce a stabilized switch engine along with other ash, making infinite growth. Until recently the only known syntheses for clean unstabilized switch engines used four or more gliders. There are several such recipes. In the reaction shown below no glider arrives from the direction that the switch engine will travel to, making it easier to repeat the reaction:
.png)
Two lines of boats (or other suitable objects, such as tub with tails) arranged so that a switch engine can travel between them, in the following manner:
quadratic growth pattern found by Michael Simkin in October 2014. Currently this is the smallest starting population (23 cells) known to result in a quadratic population growth rate. Previous record-holders include Jaws, mosquito1, mosquito2, mosquito3, mosquito4, mosquito5, teeth, catacryst, metacatacryst, Gotts dots, wedge, 26-cell quadratic growth, 25-cell quadratic growth, and 24-cell quadratic growth.
Any object which can be rotated and/or flipped over an axis and still maintain the same shape. Many common small objects such as the block, beehive, pond, loaf, clock, and blinker are symmetric. Some larger symmetric objects are Kok's galaxy, Achim's p16, cross, Eureka, and the pulsar.
Large symmetric objects can easily be created by placing multiple copies of any finite object together in a symmetrical way. Unless the individual objects interact significantly, this is considered trivial and is not considered further here (e.g., two LWSSs travelling together a hundred cells apart).
There are two kinds of symmetry. Odd symmetry occurs when an object's line of reflection passes through the center of a line of cells. Objects with odd symmetry have an odd number of columns or rows, and can have a gutter. Even symmetry occurs when the line of reflection follows the boundary between two lines of cells. Objects with even symmetry have an even number of columns or rows.
Because the Life universe and its rules are symmetric, all symmetric objects must remain symmetric throughout their evolution. Most non-symmetric objects keep their non-symmetry as they evolve, but some can become symmetric, especially if they result in a single object. Here is a slightly more complicated example where two gliders interact to form a blockade:
Many useful objects are symmetric along an orthogonal axis. This commonly occurs by placing two copies of an object side by side to change the behaviour of the objects due to the inhibition or killing of new cells at their gutter interface. Examples of this are twin bees shuttle, centinal, and the object shown in puffer. Other useful symmetric objects are created by perturbing a symmetric object using nearby oscillators or spaceships in a symmetric manner. Examples of this are Schick engine, blinker ship, and hivenudger.
Many spaceships found by search programs are symmetric because the search space for such objects is much smaller than for non-symmetrical spaceships. Examples include dart, 60P5H2V0, and 119P4H1V0.
Indicates that precise relative timing is required for two or more input signals entering a circuit, or two or more sets of gliders participating in a glider synthesis. Compare asynchronous. See also salvo and slow glider construction.
A small stable converter found by Tanner Jacobi in March 2015, accepting a glider as input and producing an output Herschel As of June 2018 it is the smallest known converter of this type, so it is very often used to handle input gliders in complex signal circuitry, as described in Herschel circuit. A second glider can safely follow the first any time after 78 ticks, but overclocking also allows the syringe to work at a repeat time of 74 or 75 ticks. If followed by a dependent conduit a simple eater2 can be used instead of the large welded catalyst shown here. A ghost Herschel marks the output location.
A different version of the large catalyst, with better clearance for some situations, can be seen in the switch entry.
The following induction coil.
= tagalong
An object which is not a spaceship in its own right, but which can be attached to one or more spaceships to form a larger spaceship. For examples see Canada goose, fly, pushalong, sidecar and sparky. See also Schick engine, which consists of a tagalong attached to two LWSS (or similar).
The following c/4 spaceship (Nicolay Beluchenko, February 2004) has two wings, either of which can be considered as a tagalong. But if either wing is removed, then the remaining wing becomes an essential component of the spaceship, and so is no longer a tagalong.
A spark at the back of a spaceship. For example, the 1-bit spark at the back of a LWSS, MWSS or HWSS in their less dense phases.
To perturb a dirty reaction using other patterns so as to make it clean and hopefully useful. Or to make a reaction work which would otherwise fail due to unwanted products which interfere with the reaction.
See tame.
Two gliders travelling on parallel lanes at a fixed spacetime offset, usually as a single signal in a Herschel transceiver. See also glider pair.
An oscillator found by Tanner Jacobi on 20 October 2017. This oscillator hassles an evolving pi-heptomino to produce an phi spark. The spark is very accessible and is able to perturb many things.
The period of this new oscillator is the same as the old twin bees shuttle, and so this is able to expand the known p46 technology. For example, a p46 glider gun can be made from a Tanner's p46 and just one of the twin bees shuttles.
Acting on their own, two copies of Tanner's p46 placed at right angles to each other with their sparks interacting can produce two different p46 glider guns and a gliderless p46 MWSS gun. See p46 gun and gliderless for two of these. These are the first p46 guns found which do not use a twin bees shuttle at all.
A necessary component of a slow salvo recipe used by a single-arm universal constructor. A target usually consists of a single object, or sometimes a small constellation of common still lifes and/or oscillators. See intermediate target. If no hand target is available, a construction arm may be unable to construct anything, unless recipes are available to generate targets directly from the elbow.
The following induction coil, or the formation of two beehives that it evolves into after 20 generations. (Compare butterfly, where the beehives are five cells further apart.)
Found by Dave Buckingham, January 1973.
The collective set of known reactions exploiting one subset of the Life universe. Examples of these subsets include glider synthesis, period 30 glider streams, c/3 spaceships, sparkers, Herschel conduits, and slow salvos. As new reactions and objects are found, over time any particular technology becomes more versatile and complete. Many Life experts like to concentrate on particular technologies.
A head-on collision between three gliders, producing a perpendicular output glider that can be used to construct closely spaced glider salvos, or to inject a glider into an existing stream. There are several workable recipes. One of the more useful is the following, because the tandem glider can be generated by a small Herschel converter, SW1T43:
A 65-cell quadratic growth pattern found by Nick Gotts in March 2000. This (and a related 65-cell pattern which Gotts found at about the same time) beat the record previously held by mosquito5 for smallest population known to have superlinear growth, but was later superseded by catacryst. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
A pattern created by Jason Summers in February 2003. It transmits and receives information using a rare type of reburnable fuse, a lightspeed wire made from a chain of beehives, at the rate of 1440 ticks per bit. The rate of travel of signals through the entire transceiver device can be increased to any speed strictly less than the speed of light by increasing the length of the beehive chain appropriately.
"Telegraph" may also refer to any device that sends and receives lightspeed signals; see also p1 telegraph, high-bandwidth telegraph.
Any reaction between three objects. In particular, a reaction in which two gliders from one stream and one glider from a crossing stream of the same period annihilate each other. This can be used to combine two glider guns of the same period to produce a new glider gun with double the period.
Any 4-cell polyplet.
Any 4-cell polyomino. There are five such objects, shown below. The first is the block, the second is the T-tetromino and the remaining three rapidly evolve into beehives.
A distributed search effort set up by Nathaniel Johnston in 2009, using a Python script running in Golly. Results included a collection of the longest-lived 20×20 soups, as well as a census of over 174 billion ash objects. It has since been superseded by Catagolue.
A popular science book by William Poundstone (1985) dealing with the nature of the universe, illuminated by parallels with the game of Life. This book brought to a wider audience many of the results that first appeared in LifeLine. It also outlines the proof of the existence of a universal constructor in Life first given in Winning Ways.
A spark-like protrusion which flicks out in a manner resembling a thumb being flicked. Below on the left is a p9 thumb sparker found by Dean Hickerson in October 1998. On the right is a p4 example found by David Eppstein in June 2000.
A term used in naming certain still lifes (and the stator part of certain oscillators). It indicates that the object consists of two smaller objects joined point to point, as in ship tie boat.
The following pattern by Doug Petrie, which is really just a glider-producing switch engine in disguise. See infinite growth for some better examples of a similar nature.
The superstring with the following repeating segment. The front part becomes p16, but the eventual fate of the detached back part is unknown.
Found by Robert Wainwright in October 1989. See also filter.
Found by Nicolay Beluchenko in April 2005.
Found by Achim Flammenkamp in September 1994. There is also a much larger and fully symmetric version found by Flammenkamp in August 1994.
Found by Simon Norton, May 1970. This is the second most common oscillator, although blinkers are more than a hundred times as frequent. See also killer toads. A toad can be used as a 90-degree one-time turner.
The protruding cells at the edges can perturb some reactions by encouraging and then suppressing births on successive ticks. For example, a toad can replace the northwest eater in the Callahan G-to-H converter, allowing it to be packed one diagonal cell closer to other circuits.
A toad hassler that works in the manner of the following example. Two domino sparkers, here pentadecathlons, apply their sparks to the toad in order to flip it over. When the sparks are applied again it is flipped back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-flipper will still work, but because of symmetry there are really only two different types. Compare toad-sucker.
A toad hassler that works in the manner of the following example. Two domino sparkers, here pentadecathlons, apply their sparks to the toad in order to shift it. When the sparks are applied again it is shifted back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-sucker will still work, but because of symmetry there are really only three different types. Compare toad-flipper.
Found by Dean Hickerson, April 1992.
Any gun that can be turned off or turned on by the same external signal - the simplest possible switching mechanism. An input signal causes the gun to stop producing gliders. Another input signal from the same source restores the gun to its original function. Compare switchable gun.
Here's a small example by Dean Hickerson from September 1996:
...............O..O....b......... .OOOO..............O..b.......... O...O..........O...O..bbb........ ....O...........OOOO............. O..O........................aaa.. ............................a.... .............................a...In the figure above, glider B and an LWSS are about to send a glider NW. Glider A will delete the next glider after B, turning off the output stream. But if the device were already off, B wouldn't be present and A would instead delete the leading LWSS, turning the device back on.
Any signal-processing circuit that switches back and forth between two possible states or outputs. An early example is the boat-bit. More recent discoveries include the semi-Snarks, which alternate between reflecting and absorbing input gliders. The following B-to-G converter sends alternate glider outputs in opposite directions.
Acronym for The Online Life-Like CA Soup Search.
A set of Life reactions and mechanisms that can be used to solve any problem in a specific pre-defined class of problems: glider timing adjustment, salvo creation, seed construction, etc. See also universal toolkit, technology.
As applies to Life, usually means a finite Life universe which takes the form of an m × n rectangle with the bottom edge considered to be joined to the top edge and the left edge joined to the right edge, so that the universe is topologically a torus. There are also other less obvious ways of obtaining a toroidal universe.
See also Klein bottle. Every object in a torus universe obviously either dies or becomes a still life or oscillator.
Any finite pattern which evolves in such a way that no cell in the Life plane is eventually periodic. The first example was found by Bill Gosper in November 1997. A few days later he found the following much smaller example consisting of three copies of a p12 backrake by Dave Buckingham.
Conway's name for the following pentomino, which is a common parent of the T-tetromino.
A path made out of conduits, often ending where it begins so that the active signal object is cycled forever, forming an oscillator or a gun.
This term has also been used to refer to the lane on which a glider or spaceship travels. The concept is very similar, but a reference to a "track" now usually implies a non-trivial supporting conduit.
A stream of spaceships that can draw an object towards the source of the stream. The example below shows a tractor beam pulling a loaf; this was used by Dean Hickerson to construct a sawtooth.
Any traffic light hassler, such as traffic circle. The term is also applied to the following reaction, used in most traffic light hasslers, in which two traffic lights interact in such a way as to reappear after 25 generations with an extra 6 spaces between them. See traffic lights extruder for a way to make this reaction extensible.
A common formation of four blinkers.
A growing pattern constructed by Jason Summers in October 2006, which slowly creates an outward-growing chain of traffic lights. The growth occurs in waves which travel through the chain from one end to the other. It can be thought of as a complex fencepost for a wick that does not need a wickstretcher.
The following illustrates the reaction used, in which a newly created traffic light at the left eventually pushes the rightmost one slightly to the right.
In signal circuitry, a term used for a catalyst that is completely destroyed by the passing signal, then rebuilt. Often (though not always) the active reaction passes directly through the area occupied by the transparent catalyst, then rebuilds the catalyst behind itself, as in the transparent block reaction. See also transparent lane.
A certain reaction between a block and a Herschel predecessor in which the block reappears in its original place some time later, the reaction having effectively passed through it. This reaction was found by Dave Buckingham in 1988. It has been used in some Herschel conduits, and in the gunstars. Because the reaction involves a Herschel predecessor rather than an actual Herschel, the following diagram shows instead a B-heptomino (which by itself would evolve into a block and a Herschel).
A mechanism where a Herschel or other active reaction completely destroys a catalyst in a particular location in a conduit. After passing through or past that location, the same reaction then recreates the catalyst in exactly its original position. This type of catalysis is surprisingly common in signal circuitry. For an example, see transparent block reaction.
The transparent object is most often a very common still life such as a block or beehive. Rarer objects are not unknown; for example, a transparent loaf was found by Stephen Silver in October 1997, in a very useful elementary conduit making up part of a Herschel receiver. However, not surprisingly, rarer objects are much less likely to reappear in exactly the correct location and orientation, so transparent reactions involving them are much more difficult to find, on average.
A path through a signal-producing circuit that can be used to merge signal streams. The signal is usually a standard spaceship such as a glider. It can either be produced by the circuit, or it can come from elsewhere, passing safely through on the same lane without interacting with the circuit. A good example is the NW31 converter, which has two glider outputs on transparent lanes:
The optional third output shown in NW31 is non-transparent, because the upper eater1 catalyst would get in the way of a passing glider on the same lane.
A colour-preserving period-multiplying signal conduit found by Tanner Jacobi on 7 September 2017, producing one output glider for every three input gliders. It uses the same block-to-pre-honeyfarm bait reaction as the Snark, and so has the same 43-tick recovery time. Compare semi-Snark.
Found by Robert Wainwright, February 1982. In terms of its 7×7 bounding box this ties with jam as the smallest p3 oscillator.
A signal, usually a single glider, that collides with a seed constellation to produce a relatively rare still life or oscillator, or an output spaceship or other signal. The constellation is destroyed or damaged in the process; compare circuit, reflector. Here a pair of trigger gliders strike a dirty seed constellation assembled by Chris Cain in March 2015, to launch a three-engine Cordership:
"Trigger" is also used when a spaceship reacts with another object to cause a reaction to occur whenever desired (but perhaps only at particular intervals). The object being triggered lies dormant until the reaction is required. All turners and freeze-dried constellations are triggerable.
In some cases the object is not destroyed so that the reaction can be repeated after some repeat time. See for example converter and reflector, and more specifically MWSS out of the blue and queen bee shuttle pair.
Either of the two 3-cell polyominoes. The term is rarely used in Life, since the two objects in question are simply the blinker and the pre-block.
Found by Dean Hickerson, October 1989. Compare caterer and double caterer.
The following pattern, found by Gabriel Nivasch in July 2001. It is unique among 32-bit still lifes in that it can be broken down into three stable pieces but not into two. The term may also refer to any larger stable pattern with the same property. See also quad pseudo.
Any 3-cell polyplet. There are 5 such objects, shown below. The first two are the two triominoes, and the other three vanish in two generations.
The barberpole of length 3.
Found by Dave Buckingham, October 1977.
A trivial period-N oscillator is one in which every cell oscillates at some smaller factor of N. See omniperiodic. For example, the joining of a period 3 and a period 4 oscillator as shown below creates a single object which is a trivial oscillator of period 12.
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"Trivial" is also used to describe a parent of an object which has groups of cells that can be removed without changing the result, such as isolated faraway cells. For example, here is a trivial parent of a block.
.png)
An oscillator found by Dean Hickerson in December 1994. Every cell has period less than 6, so this is a trivial oscillator. It is unusual because it has period-2 cells in contact with period-3 cells.
An arrangement of four 90-degree reflectors that can be placed into the path of a glider so as to delay it by an adjustable number of generations, without changing its lane. More generally, any combination of circuits may be referred to as a trombone slide, if the grouping can be moved as a single unit that functions as a 180-degree glider reflector.
The smallest known trombone slides are made using Snarks. In the trombone slide shown below, sample input and output gliders are shown. The input glider will reach the same output location 128 generations sooner if the trombone slide is removed.
If the top and left Snarks are moved together diagonally to the upper left by N cells, then the glider delay is increased by 8N generations since the glider has to travel N more cells in each direction. This sliding action gives the trombone slide its name. If only the final Snark is moved, then the output glider's path can be altered by a number of full diagonals.
Trombone slides made of the same type of component cannot alter the glider path by half-diagonals, and can only change the timing by multiples of 8 generations. For other timing changes, different components are necessary. These may be stable like the Silver reflector or the colour-changing example shown in the reflector article, or periodic like the various bumpers.
Opposite of pseudo. A gun emitting a period n stream of spaceships (or rakes) is said to be a true period n gun if its mechanism oscillates with period n. The same distinction between true and pseudo also exists for puffers. An easy way to check that a gun is true period n is to stop the output with an eater, and check that the result is a period-n oscillator.
True period n guns are known to exist for all periods greater than 61 (see My Experience with B-heptominos in Oscillators), but only a few smaller periods have been achieved, namely 20, 22, 24, 30, 36, 40, 44, 45, 46, 48, 50, and 54 through 61. See also Quetzal for the 54-61 range.
------------------------------------ Period Discoverers Date ------------------------------------ 20 Matthias Merzenich May 2013 Noam Elkies 22 David Eppstein Aug 2000 Jason Summers 24 Noam Elkies Jun 1997 30 Bill Gosper Nov 1970 36 Jason Summers Jul 2004 40 Adam P. Goucher Mar 2013 Matthias Merzenich Jason Summers 44 Dave Buckingham Apr 1992 45 Matthias Merzenich Apr 2010 46 Bill Gosper 1971 48 Noam Elkies Jun 1997 50 Dean Hickerson Oct 1996 Noam Elkies Dave Buckingham 54 Dieter Leithner Jan 1998 Noam Elkies Dave Buckingham 55 Stephen Silver Oct 1998 56 Dieter Leithner Jan 1998 Dave Buckingham Noam Elkies 57 Matthias Merzenich Apr 2016 58 'thunk' Apr 2016 Matthias Merzenich Chris Cain 59 Adam P. Goucher Dec 2009 Jason Summers 60 Bill Gosper Nov 1970 61 Luka Okanishi Apr 2016 ------------------------------------
The following common predecessor of a traffic light.
Found by Robert Wainwright before June 1972.
A pattern that consumes the output of a tubstretcher. The smallest known tubeater was found by Nicolay Beluchenko (September 2005), and is shown below in conjunction with the smallest known tubstretcher.
Any wickstretcher in which the wick is two diagonal lines of cells forming, successively, a tub, a barge, a long barge, etc. The first one was found by Hartmut Holzwart in June 1993, although at the time this was considered to be a boatstretcher (as it was shown with an extra cell, making the tub into a boat). The following small example is by Nicolay Beluchenko (August 2005), using a quarter.
In October 2005, David Bell constructed an adjustable high-period diagonal c/4 rake that burns tubstretcher wicks to create gliders, which are then turned and duplicated by convoys of diagonal c/4 spaceships to re-ignite the stabilized ends of the same wicks.
The following 8-cell still life. See eater for a use of this object.
= tagalong
The smallest known p14 oscillator. Found by George Collins in 1970. The oscillator generates domino sparks, but they are fragile and no use has been found for them to date. In each domino, one cell is "held" (remains alive) for two generations, the other for three. By contrast, useful domino sparks are usually alive for only one tick per oscillator period.
A T-tetromino hassled by two figure-8s. Found by Robert Wainwright.
See universal computer.
A one-time glider reflector, or in other words a single-glider seed (the term is seldom or never used in relation to spaceships other than gliders). One-time turners may be 90-degree or 180-degree, or they may be 0-degree with the output in the same direction as the input. A reusable turner would instead be called a reflector. Shown on the top row below are the four 90-degree turner reactions that use common small ash objects: boat, eater1, long boat, and toad.
Of the reactions on the first row, the glider output is the same parity for all but the long boat. The three still lifes are all colour-changing, but the toad happens to be a colour-preserving turner. The third row shows an aircraft carrier serving as a "0-degree turner" that is also colour-changing.
Three of the simplest 180-degree turners are shown in the second row. The Blockic 180-degree turner is colour-preserving. The long boat and long ship are again colour-changing; this is somewhat counterintuitive as the output glider is on exactly the same lane as the input glider, but gliders travelling in opposite directions on the same lane always have opposite colours.
Many small one-time turner constellations have also been catalogued. The 90-degree two-block turner on the right, directly below the toad, is also colour-changing but has the opposite parity.
A one-time turner reaction can be used as part of a glider injection mechanism, or as a switching mechanism for a signal. If a previous reaction has created the sacrificial object, then a later glider is turned onto a new path. Otherwise it passes through the area unaffected. This is one way to create simple switching systems or logic circuits. An example is shown in demultiplexer.
Found by Dean Hickerson, October 1989.
A spaceship found by Dean Hickerson in August 1989 that produces a domino spark at the back. Hickerson used this spark to convert an approaching HWSS into a loaf, as part of the first sawtooth. (Also see tractor beam). The shape of the back end of the turtle is distinctive. Very similar but wider back ends have been found in other c/3 ships to produce period 9 and 15 spaceships.
Found by Bill Gosper in 1971, this was the basis of all known true p46 guns, and all known p46 oscillators except for glider signal loops using Snarks, until the discovery of Tanner's p46 in 2017. See new gun for an example. There are numerous ways to stabilize the ends, two of which are shown in the diagram. On the left is David Bell's double block reaction (which results in a shorter, but wider, shuttle than usual), and on the right is the stabilization by a single block. This latter method produces the very large twin bees shuttle spark which is useful in a number of ways. See metamorphosis for an example. Adding a symmetrically placed block below this one suppresses the spark. See also p54 shuttle.
Any arrangement of two twin bees shuttles such that they interact. There are many ways that the two shuttles can be placed, either head-to-head, or else at right angles. Glider guns can be constructed in at least five different ways. Here is one by Bill Gosper in which the shuttles interact head-to-head:
The large and distinctive long-lived spark produced, most commonly, by the twin bees shuttle. It starts off as shown below.
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Since the spark is isolated and long-lived, there are many possible perturbations that it can perform. One of the most useful is demonstrated in metamorphosis where a glider is converted into a LWSS. Another useful one can turn a LWSS by 90 degrees:
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= twinhat
Found by Robert Wainwright. This is a pre-pulsar hassled by killer toads.
= eater5
The type of universal constructor exemplified by the original Gemini spaceship, where two independently programmed construction arms sent gliders in pairs on 90-degree paths to collide with each other at the construction site. Construction recipes for two-arm constructors are much more efficient in general, but they require many more circuits and multiple independent data streams, which both tend to increase the complexity of self-constructing circuitry. Compare single-arm.
= duoplet.
Found by Bill Gosper, September 1971.
Found by Dave Buckingham, July 1973. Compare pulsar quadrant.
Death of a cell caused by it having fewer than two neighbours. See also overpopulation.
A rectangular pattern, of size greater than 1×1, that can simulate Life in the following sense. The pattern by itself represents a dead Life cell, and some other pattern represents a live Life cell. When the plane is tiled by these two patterns (which then represent the state of a whole Life universe) they evolve, after a fixed amount of time, into another tiling of the plane by the same two patterns which correctly represents the Life generation following the one they initially represented.
It is usual to use the prefix "meta-" for simulated Life features, so, for example, for the first known unit Life cell (constructed by David Bell in January 1996), one metatick is 5760 ticks, and one metacell is 500×500 cells. Capital letters were originally used to make this distinction - e.g., Generation, Cell - but this usage is no longer common.
In December 2005, Jason Summers constructed an analogous unit cell for Wolfram's Rule 110, a one-dimensional cellular automaton that is known be universal. See also OTCA metapixel, p1 megacell.
See universal computer, universal constructor, universal toolkit.
A computer that can compute anything that is computable. (The concept of computability can be defined in terms of Turing machines, or by Church's lambda calculus, or by a number of other methods, all of which can be shown to lead to equivalent definitions.) The relevance of this to Life is that both Bill Gosper and John Conway proved early on that it is possible to construct a universal computer in the Life universe. (To prove the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start.) Conway's proof is outlined in Winning Ways, and also in The Recursive Universe.
Until recently, no universal Life computer had ever been built in practice In April 2000, Paul Rendell completed a Turing machine construction (see http://rendell-attic.org/gol/tm.htm for details). This, however, has a finite tape, as opposed to the infinite tape of a true Turing machine, and is therefore not a universal computer. But in November 2002, Paul Chapman announced the construction of a universal computer, see http://www.igblan.free-online.co.uk/igblan/ca/. This is a universal register machine based around Dean Hickerson's sliding block memory.
In 2009 Adam P. Goucher constructed a programmable Spartan universal computer/constructor pattern using stable Herschel circuitry. It included memory tapes and registers capable of holding a simple universal instruction set and program data, and also a minimal single-arm universal constructor. Its size meant that it was extremely impractical to program it to be self-constructing, though this was theoretically possible if the escape of large numbers of gliders could be allowed as a side effect.
In February 2010, Paul Rendell completed a universal Turing machine design with an unlimited tape, as described in his thesis at http://eprints.uwe.ac.uk/22323/1/thesis.pdf.
In 2016 Nicolas Loizeau ("Coban") completed a Life pattern emulating a complete 8-bit programmable computer.
See also universal constructor.
A pattern that is capable of constructing almost any pattern that has a glider synthesis. This definition is a bit vague. A precise definition seems impossible because it is not known, for example, whether all still lifes are constructible. In any case, a universal constructor ought to be able to construct itself in order to qualify as such.
An outline of Conway's proof that such a pattern exists can be found in Winning Ways, and also in The Recursive Universe. The key mechanism for the production of gliders with any given path and timing is known as side-tracking, and is based on the kickback reaction. A universal constructor designed in this way can also function as a universal destructor: it can delete almost any pattern that can be deleted by gliders.
In May 2004, Paul Chapman and Dave Greene produced a prototype programmable universal constructor. This is able to construct objects by means of slow glider constructions. It likely that it could be programmed to construct itself, but the necessary program would be very large; moreover an additional mechanism would be needed in order to copy the program.
A universal constructor is theoretically most useful when attached to a universal computer, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows I will assume that a universal constructor always includes this computer.
The existence of a universal constructor/destructor has a number of theoretical consequences.
For example, the constructor could be programmed to make copies of itself. This is a replicator.
The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large, very high period) spaceship. Any translation is possible, so that the spaceship could travel in any direction. If the constructor makes a rotated but unreflected copy of itself, the result would be a looping spaceship or reflectorless rotating oscillator.
The constructor could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a puffer.
It is also possible to show that the existence of a universal constructor implies the existence of a stable reflector. This proof is not so easy, however, and is no longer of much significance now that explicit examples of such reflectors are known.
Progressively smaller universal-constructor mechanisms without an attached universal computer have been used in the linear propagator, spiral growth pattern, and the Demonoids and Orthogonoid. See also single-channel.
Another strange consequence of the existence of universal constructors was pointed out by Adam P. Goucher and Tanner Jacobi in 2015. Any glider-constructible pattern, no matter how large, can be constructed with a fixed number of gliders, by working out a construction recipe for a universal constructor attached to a decoder that measures the distance to a faraway object. The object's position encodes a numeric value that can be processed to retrieve as many bits of information as are needed to build a slow salvo to construct any given target pattern. The simplest design, requiring less than a hundred gliders, is described in reverse caber tosser.
= URM
A regulator in which the incoming gliders are aligned to period 1, that is, they have arbitrary timing (subject to some minimum time required for the regulator to recover from the previous glider).
Paul Chapman constructed the first universal regulator in March 2003. It is adjustable, so that the output can be aligned to any desired period. A stable universal regulator was constructed by Dave Greene in September 2015, with a minimum delay between test signals of 1177 ticks. Later stable versions have reduced the delay to 952 ticks.
A universal regulator can allow two complex circuits to interact safely, even if they have different base periods. For example, signals from a stable logic circuit could be processed by a period-30 mechanism, though the precise timing of those signals would change in most cases.
A set of Life reactions and mechanisms that can be used to construct any object that can be constructed by glider collisions. Different universal toolkits were used to construct the linear propagator, 10hd Demonoid, 0hd Demonoid, and Orthogonoid, for example.
The topology of the cells in the Life grid. In the normal universe (the usual Life arena), the grid is infinite in both directions. In a cylindrical universe, the grid is finite in one direction, and the cells at the two edges are adjacent to each other. In a torus universe, the grid is finite in both directions, and the cells at the top and bottom edges are adjacent, and the cells at the left and right edges are adjacent. There are several other more obscure types of universe.
Objects found in the cylindrical and toroidal universes can also run in the normal universe if an infinite number of copies are arranged to support each other. Sometimes the objects can be supported in other ways to make a useful finite object. This is one reason that soup searches are run in alternative universes, to find such objects.
Two blocks eating a long barge. This is a useful sparker, found by Dave Buckingham in February 1976. The name derives from the fact that it was for some time the mascot of the Unix lab of the mathematics faculty at the University of Waterloo.
An object whose fate is in some way unanswerable with our current knowledge. The simplest way that the fate of an object can be unknown involves the question of whether or not it exhibits infinite growth. For example, the fate of the Fermat prime calculator is currently unknown, but its behaviour is otherwise predictable.
A different type of unknown fate is that of the Collatz 5N+1 simulator, which may become stable, or an oscillator, or have an indefinitely growing bounding box. Its behavior is otherwise predictable, and unlike the Fermat prime calculator the population is known to be bounded.
Life objects having even worse behaviour (e.g. chaotic growth) are not known as of July 2018.
Conway's name for the following pentomino, which rapidly dies.
A universal register machine, particularly Paul Chapman's Life implementation of such a machine. See universal computer for more information.
Empty space. That is, space containing only dead cells.
The p2 agar obtained by using the pattern O..O to tile the plane. Period 2 stabilizations of finite patches of this agar are known.
The following induction coil.
of its rotor divided by the sum of the sizes of its rotor and its stator. In other words, it is the proportion of cells involved in the oscillator which actually oscillate. For many periods there are known oscillators with volatility 1, see for example Achim's p16, figure-8, Kok's galaxy, mazing, pentadecathlon, phoenix, relay, smiley and tumbler. Such an oscillator of period 3 was found in August 2012 by Jason Summers.
The smallest period for which the existence of such statorless oscillators is undecided is 7. There are oscillators with volatility arbitrarily close to 1 for all but finitely many periods, because of the possibility of feeding the gliders from a true period n gun into an eater.
The term "volatility" is due to Robert Wainwright. See also strict volatility.
Any of a number of p5 oscillators which produce sparks. See lightweight volcano, middleweight volcano and heavyweight volcano.
The set of all cells that are orthogonally adjacent to a cell or group of cells. The von Neumann neighbourhood of a cell can be thought of as the points at a Manhattan distance of 1 from that cell. Compare Moore neighbourhood.
Cell neighbourhoods can also be defined with a higher range. The von Neumann neighbourhood of range n can be defined recursively as the von Neumann neighbourhood of the von Neumann neighbourhood of range n-1. For example, the von Neumann neighbourhood of range 2 is the set of all cells that are orthogonally adjacent to the range-1 von Neumann neighbourhood.
Conway's name for the following pentomino, a loaf predecessor.
A common three-bit polyplet spark, produced most notably by the pentadecathlon.
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A small p4 c/4 diagonal tagalong that has 7 cells in every phase. It is shown here attached to the back of a Canada goose.
A fuse discovered by Earl Abbe, published in LifeLine Vol 3, September 1971.
Found by Robert Wainwright before June 1972.
The following spaceship which produces a domino spark at the back. It is useful for perturbing other objects. Found by David Bell, March 1998.
A self-supporting oblique macro-spaceship constructed by Brett Berger on December 28, 2014. It is currently the fastest oblique macro-spaceship in Conway's Game of Life by several orders of magnitude, and is also the smallest known oblique macro-spaceship in terms of bounding box, superseding the Parallel HBK. It is no longer the smallest or fastest oblique spaceship due to the discovery in 2018 of the elementary knightship Sir Robin.
Previous oblique spaceships, the Gemini and the half-baked knightships, are stationary throughout almost all of their life cycles, as they construct the necessary mechanisms to support a sudden short move. The waterbear constructs support for reburnable fuse reactions involving (23,5)c/79 Herschel climbers that are in constant motion.
A wick-like structure attached at both ends to moving spaceship-like patterns, in such a way that the entire pattern is mobile. Especially if the wave gets longer over time, the supporting patterns are wavestretchers.
Also, the gliders or spaceships emitted by a rake may be referred to as a wave, again because the line as a whole appears to move in a different direction from the individual components, due to the rake's movement. Compare with stream.
In general a wave can be interpreted as moving at a variety of different velocities, depending on which specific subcomponents are chosen as the starting and ending points for calculating speed and direction. See antstretcher, wavestretcher for a practical example of identical wave ends being connected to spaceships with different velocities.
Found by Dave Buckingham, 1976 or earlier.
= superstring.
A spaceship pattern that supports a connection to an extensible periodic wick-like structure, whose speed and/or direction of propagation are different from those of the wavestretcher spaceship.
Connecting the following to a standard diagonal antstretcher creates a new oblique wavestretcher (a type of growing spaceship) and also an alternate space nonfiller mechanism.
A 26-cell quadratic growth pattern found by Nick Gotts in March 2006, based on ideas found in metacatacryst and Gotts dots. It held the record for the smallest-population quadratic growth pattern for eight years, until it was surpassed by 25-cell quadratic growth. See switch-engine ping-pong for the lowest-population superlinear growth pattern as of July 2018, along with a list of the record-holders.
= wedge.
Found by David Eppstein in January 2000. In April 2000 Stephen Silver found a tagalong for a pair of weekenders. At present, n weekenders pulling n-1 tagalongs constitute the only known spaceships of this speed or period, except for variants of the weekender distaff that suppress its output gliders.
The first orthogonal 2c/7 rake, constructed by Ivan Fomichev on May 22nd, 2014. It uses the weak sparks from weekenders to perturb an LWSS into an active reaction in a variable-period loop, which produces a series of slow salvo gliders that finally rebuilds the LWSS.
To join two or more still lifes or oscillators together. This is often done in order to fit the objects into a smaller space than would otherwise be possible. The simplest useful example is probably the integral sign, which can be considered as a pair of welded eater1s.
One of Martin Gardner's books (1983) that collects together material from his column in Scientific American. The last three chapters of this book contain all the Life stuff.
Found by Dave Buckingham, July 1977.
A stable or oscillating linearly repeating pattern that can be made to burn at one end. See fuse. Wicks are often fairly dense, with repeating units directly connected or at least adjacent to each other, as in the beehive lightspeed wire for example. However, sparse wicks such as the blocks in the 31c/240 Herschel-pair climber are known, and arbitrarily sparse wicks can be constructed.
A spaceship-like object which stretches a wick that is fixed at the other end. The wick here is assumed to be in some sense connected, otherwise most puffers would qualify as wickstretchers. The first example of a wickstretcher was found in October 1992 (front end by Hartmut Holzwart and back end by Dean Hickerson) and stretches ants at a speed of c/4. This is shown below with an improved back end found by Hickerson the following month.
Diagonally moving c/4 and c/12 wickstretchers have also been built: see tubstretcher and linestretcher. In July 2000 Jason Summers constructed a c/2 wickstretcher, stretching a p50 traffic jam wick, based on an earlier (October 1994) pattern by Hickerson. A c/5 diagonal wickstretcher was found in January 2011 by Matthias Merzenich, who also discovered a c/5 orthogonal wickstretcher two years later in March 2013.
Any extensible tagalong or component that can be attached to itself, as well as to the back of a spaceship. The number of generations that it takes for the component to occur again in the same place is often called the period of the wicktrailer. This has little relation to the period of the component. See branching spaceship for an example of a wicktrailer that is part of a p2 spaceship, but repeats itself in the same location at period 20.
Found by Dean Hickerson, November 1989.
The following induction coil. This is generation 2 of block and glider.
In an unrelated use, "wing" may also refer to an arm of a spaceship.
Jason Summers' GUI version of lifesrc for MS Windows. It is available from http://entropymine.com/jason/life/software/.
by Elwyn Berlekamp, John Conway and Richard Guy on mathematical games. The last chapter of the second volume concerns Life, and outlines a proof of the existence of a universal constructor.
A repeating stable structure, usually fairly dense, that a signal can travel along without making any permanent change. Known wires include the diagonal 2c/3 wire, and orthogonal lightspeed wire made from a chain of beehives. Diagonal lightspeed wires are known, but the required signals are fairly complex and have no known glider synthesis.
A term used for negative spaceships travelling in zebra stripes agar, parallel to the stripes, and also for with-the-grain grey ships.
Below are three small examples of "negative spaceships" found by Gabriel Nivasch in July 1999, travelling with the grain through a stabilized finite segment of zebra stripes agar:
A grey ship in which the region of density 1/2 consists of lines of ON cells lying parallel to the direction in which the spaceship moves. See also against-the-grain grey ship.
Found by Dave Buckingham in 1972. Unlike the similar snacker this produces no sparks, and so is not very important. Like the snacker, the worker bee is extensible. It is, in fact, a finite version of the infinite oscillator which consists of six ON cells and two OFF cells alternating along a line. Note that Dean Hickerson's new snacker ends also work here.
Conway's name for the following pentomino, a common loaf predecessor.
Any of the standard orthogonal spaceships - LWSS, MWSS, or HWSS. At one point the term fish was more common for this group of spaceships.
Found by Hartmut Holzwart, July 1992. Half of this can be escorted by an HWSS. The name refers to the fact that every cell (live or dead) has at most 6 live neighbours (in contrast to spaceships based on LWSS, MWSS or HWSS). In fact this spaceship was found by a search with this restriction.
A popular freeware Life program that runs under the X Window System. The main Life code was written by Jon Bennett, and the X code by Chuck Silvers.
Conway's name for the following pentomino, a traffic light predecessor.
Conway's name for the following pentomino, which rapidly dies.
A stable agar consisting of alternating bands of live and dead cells. Known spacefillers and many gray ships create patches of this agar. It is also the medium through which with the grain and against the grain negative spaceships travel. Many simple stabilizations of the boundaries of finite regions of this agar are known, as shown below.
The following hexomino. The Z-hexomino features in the pentoad, and also in Achim's p144.
The set of cells on which a chosen cell or pattern can potentially exert an influence in a given number of generations N. If N is not specified it is generally taken to be one, in which case the zone of influence simply coincides with the Moore neighbourhood of the cell or pattern.
The set for N generations consists of all the cells to which at least N paths of length N can be traced from the cell(s) in question. Contrast this with the range-N Moore neighbourhood, which consists of all cells to which at least one path of length n can be traced.
Conway's name for the following pentomino, which rapidly dies.
An oscillator in which two HW volcanoes hassle a loaf. This was found by Mark Niemiec in February 1995. A smaller version using Scot Ellison's reduced HW volcano is shown below.
David I. Bell, Spaceships in Conway's Life. Series of articles posted on comp.theory.cell-automata, Aug-Oct 1992. Now available from his website.
David I. Bell, Speed c/3 Technology in Conway's Life, 17 December 1999. Available from his website.
Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, Winning Ways for your Mathematical Plays, II: Games in Particular. Academic Press, 1982.
David J Buckingham, Some Facts of Life. BYTE, December 1978.
Dave Buckingham, My Experience with B-heptominos in Oscillators. 12 October 1996. Available from Paul Callahan's website.
David J. Buckingham and Paul B. Callahan, Tight Bounds on Periodic Cell Configurations in Life. Experimental Mathematics 7:3 (1998) 221-241. Available at http://tinyurl.com/TightBoundsOnCellConfigs.
Noam D. Elkies, The still-Life density problem and its generalizations, pp228-253 of "Voronoi's Impact on Modern Science, Book I", P. Engel, H. Syta (eds), Institute of Mathematics, Kyiv, 1998 = Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine, math.CO/9905194.
Martin Gardner, Wheels, Life, and other Mathematical Amusements. W. H. Freeman and Company, 1983.
R. Wm. Gosper, Exploiting Regularities in Large Cellular Spaces. Physica 10D (1984) 75-80.
N. M. Gotts and P. B. Callahan, Emergent structures in sparse fields of Conway's 'Game of Life', in Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life, MIT Press, 1998.
Mark D Niemiec, Life Algorithms. BYTE, January 1979.
William Poundstone, The Recursive Universe. William Morrow and Company Inc., 1985.
The Game of Life is not your typical computer game. It is a cellular automaton, and was invented by Cambridge mathematician John Conway.
This game became widely known when it was mentioned in an article published by Scientific American in 1970. It consists of a grid of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout the course of the game.
Each cell with one or no neighbors dies, as if by solitude.
Each cell with four or more neighbors dies, as if by overpopulation.
Each cell with two or three neighbors survives.
Each cell with three neighbors becomes populated.
Video’s about the Game of Life
Interesting articles about John Conway
This site is made by Edwin Martin <edwin@bitstorm.org>