The Game of Life

With thanks to John Conway

A world ... consisting of locations which may or may not be occupied by life. And time ... as many steps as you like. And a very simple set of rules ...
    At each step, life persists in any location where it is also present in two or three of the eight neighboring locations, and otherwise disappears (from loneliness or overcrowding). Life is born in any empty location for which there is life in three of the eight neighboring locations.
Got it? Simple, no? So what would life look like in such a world? Would it die out? Persist as a disordered, ever changing blob? Create stable, discrete entities? Generate particular forms in the absence of a planner, an architect, a blueprint? Does it matter what the starting conditions are?

Try it out. Clicking on locations in the world below will change them from unoccupied (red) to occupied (green), and back again, so you can start with any arrangement you like (locations on the left edge of the world have neighbors on the right, and locations on the top neighbors on the bottom, so there are always eight possibly occupied neighbors) Then click on the left button to see what happens after one time step, or on the middle button to run through ten time steps at once. You can click either button again to keep going as long as you want. There is also a control panel if you want to do some fancier things. Either way, let's go.


Sorry, but your browser isn't capable of displaying Java applets. You'll need to upgrade it and come back. In the meanwhile, you can try a non-Java based interactive version of the Game of Life elsewhere .

A moveable control panel will appear if you click the right button below the world. You can start with a random pattern by clicking on the middle button on the control panel (the slider above it lets you vary how many occupied cells occur in the random pattern). You can also vary the number of locations in the world (top slider), clear the world (top button), and vary the number of time steps you see at one time (the bottom slider) when you click the bottom button. The save button allows you to store a pattern so you can bring it back (with the recall button) to make modifications and run it again.

The bottom line? Clearly, organized forms can arise in the absence of a planner, or an architect, or a blueprint ... even from random starting points. Simple things interacting in simple ways can yield surprising forms. For a similar conclusion, using both the Game of Life and some variants of it, see Exploring Emergence by Mitchel Resnick and Brian Silverman at the MIT Media Lab.


The Game of Life was invented by John Horton Conway, a British mathematician, and described by Martin Gardner in his Mathematical Games in Scientific American in 1970 (Scientific American 223(4), October, 1970, pp 120-123). The game continues to be actively explored (see Conway's Life Miscellany for current descriptions of findings and links to other Life related websites). Games of Life: Explorations in Ecology, Evolution, and Behavior by Karl Sigmund (Penguin, 1995) provides a nice introduction to the origins and broader implications of the game (Chapter 2), including the existence of self-replicating patterns and patterns that constitute univeral computers. which together provide an intriguing argument for the inevitability of living organisms in the universe. The Game of Life is also a good introduction the field of Cellular Automata , a more general exploration of the forms of organization that emerge from simple interactions of simple elements with applicability in a variety of contexts.

Some additional relevant sites:


Created by Paul Grobstein , Deepak Kumar, and Bogdan Butoi. Java applet by Bogdan Butoi.
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