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.


:Caterpillar 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:

Game of Life pattern ’Caterpillar_(1)’

In this reaction, the pi moves forward 17 cells in the course of 45 generations, while the blinker moves back 6 cells and is rephased. This reaction has been known for many years, but it was only in September 2002 that David Bell suggested that it could be used to build a 17c/45 spaceship, based on a reaction he had found in which pi-heptominoes crawling along two rows of blinkers interact to emit a glider every 45 generations. Similar glider-emitting interactions were later found by Gabriel Nivasch and Jason Summers. The basic idea of the spaceship design is that streams of gliders created in this way can be used to construct fleets of standard spaceships which convey gliders to the front of the blinker tracks, where they can be used to build more blinkers.

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. For other Caterpillar-type constructions see Centipede, waterbear, half-baked knightship, and Caterloopillar.

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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