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)

Zweiback

An oscillator in which two HW volcanoes hassle a loaf. This was found by Mark Niemiec in February 1995. A smaller version using Scot Ellison's reduced HW volcano is shown below.

Game of Life pattern ’zweiback’

BIBLIOGRAPHY

David I. Bell, Spaceships in Conway's Life. Series of articles posted on comp.theory.cell-automata, Aug-Oct 1992. Now available from his website.

David I. Bell, Speed c/3 Technology in Conway's Life, 17 December 1999. Available from his website.

Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, Winning Ways for your Mathematical Plays, II: Games in Particular. Academic Press, 1982.

David J Buckingham, Some Facts of Life. BYTE, December 1978.

Dave Buckingham, My Experience with B-heptominos in Oscillators. 12 October 1996. Available from Paul Callahan's website.

David J. Buckingham and Paul B. Callahan, Tight Bounds on Periodic Cell Configurations in Life. Experimental Mathematics 7:3 (1998) 221-241. Available at http://tinyurl.com/TightBoundsOnCellConfigs.

Noam D. Elkies, The still-Life density problem and its generalizations, pp228-253 of "Voronoi's Impact on Modern Science, Book I", P. Engel, H. Syta (eds), Institute of Mathematics, Kyiv, 1998 = Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine, math.CO/9905194.

Martin Gardner, Wheels, Life, and other Mathematical Amusements. W. H. Freeman and Company, 1983.

R. Wm. Gosper, Exploiting Regularities in Large Cellular Spaces. Physica 10D (1984) 75-80.

N. M. Gotts and P. B. Callahan, Emergent structures in sparse fields of Conway's 'Game of Life', in Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life, MIT Press, 1998.

Mark D Niemiec, Life Algorithms. BYTE, January 1979.

William Poundstone, The Recursive Universe. William Morrow and Company Inc., 1985.

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

Implemented by Edwin Martin <>