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)

Period multiplier

A term commonly used for a pulse divider, because dividing the number of signals in a regular stream by N necessarily multiplies the period by N. The term "period multiplier" can be somewhat misleading in this context, because most such circuits can accept input streams that are not strictly periodic.

Reactions have also been found to period double or period triple the output of some rakes to create high-period rakes in a relatively small space (i.e., an exponential increase in period for a linear increase in size).

For Herschel signals and glider guns, a number of small period doubler, tripler, and quadrupler mechanisms are known. For example, the following conduit produces one output glider after accepting four input B-heptominoes, or four Herschels if a conduit such as F117 is prepended that includes the same BFx59H converter.

Game of Life pattern ’period_multiplier’

See semi-Snark and tremi-Snark for additional examples using glider streams. As of June 2018 no stable period-multiplying elementary conduits are known for a multiplication factor of five or higher, though it is easy to construct composite ones.

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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