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.

Garden of Eden

:Garden of Eden A configuration of ON and OFF cells that can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. This example was 9 × 33. In 1974 J. Hardouin-Duparc et al. at the University of Bordeaux 1 produced a 6 × 122 example. The following shows a 12 × 12 example found by Nicolay Beluchenko in February 2006, based on a 13 × 12 one found by Achim Flammenkamp in June 2004.

Game of Life pattern ’Garden_of_Eden_(1)’

Below is a 10×10 Garden of Eden found by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels in 2013 using SAT-solver techniques. An exhaustive search of 90-degree rotationally symmetric 10×10 patterns was possible because the symmetry reduces the number of unknown cells by a factor of four.

Steven Eker has since found several asymmetrical Gardens of Eden that are slightly smaller than this in terms of bounding box area. Patterns have also been found that have only Garden of Eden parents. For related results see grandparent.

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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