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.

Still life

:still life 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.

Game of Life pattern ’still_life’

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 <>