implement on a computer, and can thus typically be investigated more extensively with given computational resources.

But an obvious issue with saying that one should study systems with the simplest possible structure is that such systems might just not be capable of exhibiting the kinds of behavior that one might consider interesting—or that actually occurs in nature.

And in fact, intuition from traditional science and mathematics has always tended to suggest that unless one adds all sorts of complications, most systems will never be able to exhibit any very relevant behavior. But the results so far in this book have shown that such intuition is far from correct, and that in reality even systems with extremely simple rules can give rise to behavior of great complexity.

The consequences of this fact for computer experiments are quite profound. For it implies that there is never an immediate reason to go beyond studying systems with rather simple underlying rules. But to absorb this point is not an easy matter. And indeed, in my experience the single most common mistake in doing computer experiments is to look at systems that are vastly more complicated than is necessary.

Typically the reason this happens is that one just cannot imagine any way in which a simpler system could exhibit interesting behavior. And so one decides to look at a more complicated system—usually with features specifically inserted to produce some specific form of behavior.

Much later one may go back and look at the simpler system again. And this is often a humbling experience, for it is common to find that the system does in fact manage to produce interesting behavior—but just in a way that one was not imaginative enough to guess.

So having seen this many times I now always try to follow the principle that one can never start with too simple a system. For at worst, one will just establish a lower limit on what is needed for interesting behavior to occur. But much more often, one will instead discover behavior that one never thought was possible.

It should however be emphasized that even in an experiment it is never entirely straightforward to discover phenomena one did not expect. For in setting up the experiment, one inevitably has to make assumptions about the kinds of behavior that can occur. And if it turns

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