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.

Phase change

: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.

Game of Life pattern ’phase_change_(1)’

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).

Game of Life pattern ’phase_change_(2)’

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.

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 <>