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)

Line-mending reaction

A reaction which can fully mend a sealed gap in an infinite diagonal line of cells, such as the one produced by a line-cutting reaction. Such a reaction is demonstrated below. See the line cutting reaction for a way of creating the gliders travelling parallel to the line.

Game of Life pattern ’line-mending_reaction’

This reaction uses spaceships on both sides of the line which need to be synchronized to each other, for example by passing a glider through the gap to trigger the creation of the required spaceships and gliders.

No simple mechanism is known to mend the gap which lies completely on one side of the line. However, it is technically possible to use construction arm technology to push objects through the gap to build and trigger a seed for the required synchronized signals on the other side.

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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