Conway’s Game of Life

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Life Lexicon

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. (CC BY-SA 3.0)

Pulse divider

A mechanism that lets every n-th object that reaches it pass through, and deletes all the rest, where n > 1 and the objects are typically gliders, spaceships or Herschels. A common synonym is period multiplier. For n=2, the simplest known stable pulse dividers are the semi-Snarks.

The following diagram shows a p5 glider pulse divider by Dieter Leithner (February 1998). The first glider moves the centre block and is reflected at 90 degrees. The next glider to come along will not be reflected, but will move the block back to its original position. The relatively small size and low period of this example made it useful for constructing compact glider guns of certain periods, but it became largely obsolete with the discovery of the stable CC semi-Snark, which uses the same basic mechanism. Period 7, 22, 36 and 46 versions of this pulse divider are also known.

Game of Life pattern ’pulse_divider’

Game of Life Explanation

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 grid 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:
Examples

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.

More information

Video’s about the Game of Life

Stephen Hawkings The Meaning of Life (John Conway's Game of Life segment)
The rules are explained in Stephen Hawkings’ documentary The Meaning of Life
Inventing Game of Life (John Conway) - Numberphile
John Conway himself talks about the Game of Life

Interesting articles about John Conway

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