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)

NW31

One of the most common stable edge shooters. This Herschel-to-glider converter suppresses the junk ordinarily left behind by an evolving Herschel while allowing both the first natural glider and second natural glider to escape on transparent lanes:

Game of Life pattern ’NW31’

The edge shooter output at the top has no additional clearance, so its use in creating convoys is limited: it can only add gliders on the outermost lanes of an existing glider salvo. Like the beehive version of SW-2, either output can be used to build logical OR gates, where multiple input signal paths are merged onto the same output path.

The complete name for this converter is "NW31T120", where 31 is the output glider lane number. In the above orientation, lane numbers get bigger toward the upper right and smaller toward the lower left (and may easily be negative).

The T120 timing measurement means that a canonical NW glider placed on lane 31 at time T=120, at (+31, +0) relative to the input Herschel, would in theory reach the exact same spacetime locations as the converter's output glider does.

Most converters are not edge shooters and their output lanes are not transparent, so they usually have catalysts that would interfere with this theoretically equivalent glider. This is the case for the optional third glider output created by the lower eater1 catalyst: the upper eater1 overlaps its lane. For the alternate block catalyst suppressing this glider output, see transparent lane.

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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