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.


:symmetric 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:

Game of Life pattern ’symmetric’

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.

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.


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 <>