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)

2c/3 wire

A wire discovered by Dean Hickerson in March 1997, using his dr search program. It supports signals that travel through the wire diagonally at two thirds of the speed of light.

Game of Life pattern ’2c;3_wire’

Each 2c/3 signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.

Considerable effort has been spent on finding a way to turn a 2c/3 signal 90 or 180 degrees, since this would by one way to prove Life to be omniperiodic. There is a known 2c/3 converter shown under signal elbow, which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it can't be used to complete a loop.

Noam Elkies discovered a glider synthesis of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See stable pseudo-Heisenburp for details. On 11 September 2017, Martin Grant reduced the input reaction to five gliders, or three gliders plus a Herschel. With the Herschel option the recovery time is 152 ticks.

See also 5c/9 wire.

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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