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.

Memory cell

:memory cell A type of information storage circuit useful in many patterns that perform complex logical operations. Most commonly a memory cell can store a single bit of information. See for example demultiplexer, honey bit, and boat-bit. Depending on the application, the circuit may be a toggle circuit or a permanent switch, or it may be possible to send one or more signals to set the circuit to a "1" state, as can be done with a keeper mechanism. In that case a different input signal must be used to test the current state, usually with a destructive read reaction.

A more complicated example can be found in the Osqrtlogt pattern, which destructively reads a growing 2-dimensional array of minimal memory cells. Each memory cell may either contain a boat (below left) or empty space (below right), with no permanent circuitry anywhere near:

Game of Life pattern ’memory_cell’

The two beehives and the block are placed by slow salvos, after an initial 90-degree 2-glider collision that produces a target honey farm. The beehive constellation acts as a one-time turner for an incoming glider. If the boat is present, it acts as a second one-time turner for that glider, sending back a "1" signal. The "backstop" block in the northeast is destroyed cleanly in either the "0" or the "1" case.

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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