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)

Switch

A signal-carrying circuit that can send output signals to two or more different locations, depending on the state of the mechanism. These may be toggle circuits, where the state of the switch changes after each use, or permanent switches that retain the same state through many uses until a change is made with a separate signal.

More generally, any circuit may be referred to as a switch, if it can alter its output based on stored information. For example, the following simple mechanism based on an eater2 was discovered by Emerson J. Perkins in 2007. It either reflects or absorbs an incoming signal, depending on the presence or absence of a nearby block. The block is removed if a reflection occurs.

Game of Life pattern ’switch’

The switching signal here is a glider produced by a high-clearance syringe variant found by Matthias Merzenich. The syringe is not technically part of the switch mechanism; any standard Herschel source can deliver the signal to the block factory (the two eater1s on the right side of the pattern). Alternate converter mechanisms could also be used to place the block.

An earlier example of the same type of one-time switch mechanism, also mediated by a block, can be found in the NW34T204 H-to-G. See also bistable switch for a very robust and versatile toggle switch with two input lanes and four possible outputs.

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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