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)

Turner

A one-time glider reflector, or in other words a single-glider seed (the term is seldom or never used in relation to spaceships other than gliders). One-time turners may be 90-degree or 180-degree, or they may be 0-degree with the output in the same direction as the input. A reusable turner would instead be called a reflector. Shown on the top row below are the four 90-degree turner reactions that use common small ash objects: boat, eater1, long boat, and toad.

Game of Life pattern ’turner’

Of the reactions on the first row, the glider output is the same parity for all but the long boat. The three still lifes are all colour-changing, but the toad happens to be a colour-preserving turner. The third row shows an aircraft carrier serving as a "0-degree turner" that is also colour-changing.

Three of the simplest 180-degree turners are shown in the second row. The Blockic 180-degree turner is colour-preserving. The long boat and long ship are again colour-changing; this is somewhat counterintuitive as the output glider is on exactly the same lane as the input glider, but gliders travelling in opposite directions on the same lane always have opposite colours.

Many small one-time turner constellations have also been catalogued. The 90-degree two-block turner on the right, directly below the toad, is also colour-changing but has the opposite parity.

A one-time turner reaction can be used as part of a glider injection mechanism, or as a switching mechanism for a signal. If a previous reaction has created the sacrificial object, then a later glider is turned onto a new path. Otherwise it passes through the area unaffected. This is one way to create simple switching systems or logic circuits. An example is shown in demultiplexer.

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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