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)

Trombone slide

An arrangement of four 90-degree reflectors that can be placed into the path of a glider so as to delay it by an adjustable number of generations, without changing its lane. More generally, any combination of circuits may be referred to as a trombone slide, if the grouping can be moved as a single unit that functions as a 180-degree glider reflector.

The smallest known trombone slides are made using Snarks. In the trombone slide shown below, sample input and output gliders are shown. The input glider will reach the same output location 128 generations sooner if the trombone slide is removed.

If the top and left Snarks are moved together diagonally to the upper left by N cells, then the glider delay is increased by 8N generations since the glider has to travel N more cells in each direction. This sliding action gives the trombone slide its name. If only the final Snark is moved, then the output glider's path can be altered by a number of full diagonals.

Game of Life pattern ’trombone_slide’

Trombone slides made of the same type of component cannot alter the glider path by half-diagonals, and can only change the timing by multiples of 8 generations. For other timing changes, different components are necessary. These may be stable like the Silver reflector or the colour-changing example shown in the reflector article, or periodic like the various bumpers.

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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