Play John Conway’s Game of Life

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Life Lexicon

(CC BY-SA 3.0)

This Life lexicon is compiled by Stephen A. Silver from various sources and may be copied, modified and distributed under the terms of the Creative Commons Attribution-ShareAlike 3.0 Unported licence. See the original credit page for all credits and the original download location. The styling has been adjusted to fit this website.

Reflector

:reflector 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.

Game of Life pattern ’reflector’

John Conway’s Game of Life

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 collection 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.

Rules

For a space that is populated:

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.

For a space that is empty or unpopulated

Each cell with three neighbors becomes populated.

The Controls

Choose a pattern from the lexicon or make one yourself by clicking on the cells. The 'Start' button advances the game by several generations (each new generation corresponding to one iteration of the rules).

More information

In the first video, from Stephen Hawkings’ documentary The Meaning of Life, the rules are explained, in the second, John Conway himself talks about the Game of Life.

Stephen Hawkings The Meaning of Life (John Conway's Game of Life segment) Inventing Game of Life (John Conway) - Numberphile

The Guardian published a nice article about John Conway.


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Implemented by Edwin Martin <>