The Standing Invitation

A Toy Universe

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Conway’s Game of Life is truly a wonderful thing. It’s a computer program that models a whole universe, albeit a very simple one.

(There’s a Java version here. Have a play with it. If you want to do more, you might download Golly, found here.)

This simulated universe is two-dimensional, and consists of millions of cells arranged in squares. Each cell can be either ON (black) or OFF (white). At the start of the simulation, the user clicks some cells on or off in whatever pattern he likes, then presses ‘GO’. The computer does the rest, playing out the universe’s future step by step.

These black and white cells are governed by four simple rules:

1)   Any ON cell with fewer than two ON neighbours turns OFF in the next instant (underpopulation).

2)   Any ON cell with two or three ON neighbours remains ON in the next instant (survival).

3)   Any ON cell with more than three ON neighbours become OFF (overcrowding).

4)   Any OFF cell with three ON neighbours becomes ON (reproduction).

That’s all: these are the laws of physics of this simulated universe, much simpler than our laws about gravity and entropy. These rules are just as unbreakable in Life as in our world; it is a deterministic universe, and in that sense limited if you want to see it that way. But look what can be done within these limits.

Everything that happens is the result of these simple rules operating on cells, turning them ON or OFF, and on that level the game is uninteresting: we always know what will happen. But zoom out a bit and the cells become too small to see. Instead we see patterns of cells. Some of these patterns are not long-lived and disappear or change dramatically; but others, the interesting ones, preserve their identity, and have emergent properties of their own.

Take the ‘glider’ shown above. When this pattern appears, it cycles through four steps, eventually returning to its original shape but shifted one cell down and to the side. You could of course see it as individual cells turning ON and OFF, but it looks quite a lot like a persistent, self-contained object that flies diagonally across the screen until it hits something.

The parallels with our own world, our own lives, are striking. The atoms that make up our bodies come and go, and yet we remain. We are the patterns, not the atoms that we happen to consist of at the time.

There are people, both hobbyists and serious mathematicians, who spend their time charting the ecology of these toy universes. They have discovered or made ‘guns’ that periodically spit out gliders, or ‘puffers’ that move in one direction emitting a stream of debris.

What’s even more fascinating is that these ‘guns’ can send binary information to each other in the form of a string of gliders (a glider representing 1, the absence of one representing 0). The gliders can interact to produce logical operators – AND gates, XOR gates. In fact, it has been shown, mathematically, that it is possible to build a whole computer in Life.

Of course such a computer would be gigantic, consuming millions or billions of cells. But just think: this computer would itself be capable of running a version of Life. A simulated world inside a simulated world…

REFERENCES

http://en.wikipedia.org/wiki/Conway’s_Game_of_Life

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Written by The S I

September 4, 2011 at 11:59 pm

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