Play John Conway’s Game of Life

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Life Lexicon

(CC BY-SA 3.0)

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. The styling has been adjusted to fit this website.

Glider duplicator

:glider duplicator Any reaction in which one input glider is converted into two output gliders. This can be done by oscillators or spaceships, or by Herschel conduits or other signal circuitry such as the stable example shown under splitter. The most useful glider duplicators are those with low periods.

The following period 30 glider duplicator demonstrates a simple mechanism found by Dieter Leithner. The input glider stream comes in from the upper left, and the output glider streams leave at the upper and lower right. One of the output glider streams is inverted, so an inverting reflector is required to complete the duplicator. To produce non-parallel output, an inline inverter could be substituted for the northmost p30 glider gun.

Game of Life pattern ’glider_duplicator’

Spaceship convoys that can duplicate gliders are very useful since they (along with glider turners) provide a means to clean up many dirty puffers by duplicating and turning output gliders so as to impact into the exhaust to clean it up.

Glider duplicators and turners are known for backward gliders using p2 c/2 spaceships, and for forward gliders using p3 c/3 spaceships. These are the most general duplicators for these speeds.

John Conway’s Game of Life

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 collection 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:

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.

The Controls

Choose a pattern from the lexicon or make one yourself by clicking on the cells. The 'Start' button advances the game by several generations (each new generation corresponding to one iteration of the rules).

More information

In the first video, from Stephen Hawkings’ documentary The Meaning of Life, the rules are explained, in the second, John Conway himself talks about the Game of Life.

Stephen Hawkings The Meaning of Life (John Conway's Game of Life segment) Inventing Game of Life (John Conway) - Numberphile

The Guardian published a nice article about John Conway.


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Implemented by Edwin Martin <>