by computers whose programs in effect implement a huge variety of rules. The programs we use in practice are mostly based on extremely complicated rules specifically designed to perform particular tasks. But a program can in principle follow essentially any definite set of rules. And at the core of the new kind of science that I describe in this book are discoveries I have made about programs with some of the very simplest rules that are possible.

One might have thought—as at first I certainly did—that if the rules for a program were simple then this would mean that its behavior must also be correspondingly simple. For our everyday experience in building things tends to give us the intuition that creating complexity is somehow difficult, and requires rules or plans that are themselves complex. But the pivotal discovery that I made some eighteen years ago is that in the world of programs such intuition is not even close to correct.

I did what is in a sense one of the most elementary imaginable computer experiments: I took a sequence of simple programs and then systematically ran them to see how they behaved. And what I found—to my great surprise—was that despite the simplicity of their rules, the behavior of the programs was often far from simple. Indeed, even some of the very simplest programs that I looked at had behavior that was as complex as anything I had ever seen.

It took me more than a decade to come to terms with this result, and to realize just how fundamental and far-reaching its consequences are. In retrospect there is no reason the result could not have been found centuries ago, but increasingly I have come to view it as one of the more important single discoveries in the whole history of theoretical science. For in addition to opening up vast new domains of exploration, it implies a radical rethinking of how processes in nature and elsewhere work.

Perhaps immediately most dramatic is that it yields a resolution to what has long been considered the single greatest mystery of the natural world: what secret it is that allows nature seemingly so effortlessly to produce so much that appears to us so complex.

It could have been, after all, that in the natural world we would mostly see forms like squares and circles that we consider simple. But in fact one of the most striking features of the natural world is that

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