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)

Clock insertion

A uniquely effective method of adding a glider to the front edge of a salvo, by first constructing a clock, then converting it to a glider using a one-bit spark. Here it rebuilds a sabotaged glider in a deep pocket between other gliders:

Game of Life pattern ’clock_insertion’

In 2015 Chris Cain used this reaction to demonstrate conclusively that any unidirectional glider salvo, no matter how large or tightly packed, can be constructed by collisions between gliders that are initially separated by any finite distance. As a corollary, because all glider syntheses are made up of two to four unidirectional salvos, any glider-constructible object has a synthesis that starts with every glider at least N cells away from every other glider (for any chosen N).

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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