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)

Sawtooth

Any finite pattern whose population grows without bound but does not tend to infinity. (In other words, the population reaches new heights infinitely often, but also infinitely often returns to some fixed value.) Conway's preferred plural is "sawteeth".

The first sawtooth was constructed by Dean Hickerson in April 1991. The current smallest known sawtooth was found by a conwaylife.com forum user with the online handle 'thunk'. It has a bounding box of 74×60, and is the smallest known sawtooth in terms of its minimum repeating population of 177 cells. The following variant has a higher repeating population of 194 and an optimized bounding box of 62×56:

Game of Life pattern ’sawtooth’

Patterns combining a fast puffer with a slower spaceship have also been constructed (see moving sawtooth). See also tractor beam.

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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