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.

Partial result

:partial result An intermediate object found by a search program which might be a substantial part of a complete spaceship or oscillator, but which isn't complete.

Running a partial result works for a few generations until the speed of light corruption from any unfinished edge destroys the whole object. But a partial result can still be used to see whether the object (if ever finished) would provide a desired spark or perturbation. If no partial results are found then it is likely that no such object exists under the constraints of the search.

Very large partial results can indicate that there is a good chance that the object being searched for might actually exist (but this is no guarantee). Rerunning the search using the partial result as a base and relaxing some constraints, widening or adjusting the search area, or splitting the object into multiple arms might result in finding a complete working object.

As an example, here is a large partial result for a period 6 knightship found by Josh Ball in April 2017. The first 22 columns were rediscovered in 2018 as part of the successful search for Sir Robin. See also almost knightship for an earlier small example by Eugene Langvagen.

Game of Life pattern ’partial_result’

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 <>