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systems in which it is overwhelmingly easier to generate highly complex behavior than to recognize the origins of this behavior.

As I have discovered in this book, it is rather easy to generate complex behavior by starting from simple initial conditions and then following simple sets of rules. But the point is that if one starts from some particular piece of behavior there are in general no such simple rules that allow one to go backwards and find out how this behavior can be produced. Typically the problem is similar to trying to find solutions that will satisfy certain constraints. And as we have seen several times in this book, such problems can be extremely difficult.

So insofar as the actual processes of perception and analysis that end up being used are fairly simple, it is inevitable that there will be situations where one cannot recognize the origins of behavior that one sees—even when this behavior is in fact produced by very simple rules.

Captions on this page:

Patterns produced by taking a single black cell, then evolving for 50 and 100 steps according to outer totalistic cellular automaton rules 54, 222 and 374. Despite the simple description that can be given of this procedure, our standard methods of perception and analysis cannot readily deduce this description given just the final pictures shown here.

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