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watch what happens. And as it turns out, in the particular case shown here, the outcome is finally clear after about 2780 steps: one structure survives, and that structure interacts with the periodic stripes coming from the left to produce behavior that repeats every 240 steps.

However certain one might be that simple programs could never do more than produce simple behavior, the pictures on the past few pages [32, 33, 34, 35, 36, 37, 38] should forever disabuse one of that notion. And indeed, what is perhaps most bizarre about the pictures is just how little trace they ultimately show of the simplicity of the underlying cellular automaton rule that was used to produce them.

One might think, for example, that the fact that all the cells in a cellular automaton follow exactly the same rule would mean that in pictures like the last few pages [32, 33, 34, 35, 36, 37, 38] all cells would somehow obviously be doing the same thing. But instead, they seem to be doing quite different things. Some of them, for example, are part of the regular background, while others are part of one or another localized structure. And what makes this possible is that even though individual cells follow the same rule, different configurations of cells with different sequences of colors can together produce all sorts of different kinds of behavior.

Looking just at the original cellular automaton rule one would have no realistic way to foresee all of this. But by doing the appropriate computer experiments one can easily find out what actually happens—and in effect begin the process of exploring a whole new world of remarkable phenomena associated with simple programs.

The Need for a New Intuition

The pictures in the previous section plainly show that it takes only very simple rules to produce highly complex behavior. Yet at first this may seem almost impossible to believe. For it goes against some of our most basic intuition about the way things normally work.

Captions on this page:

A single picture of the behavior from the previous five pages [33, 34, 35, 36, 37]. A total of 3200 steps are shown. Note that this is more than twice as many as in the picture on page 30.

From Stephen Wolfram: A New Kind of Science [citation]