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The pictures on the facing page show what happens if one starts with a single circle, then successively adds new circles in such a way that the center of each one is as close to the center of the first circle as possible. When all circles are the same size, this procedure yields a simple repetitive pattern. But as soon as the circles have significantly different sizes, the pictures on the facing page show that this procedure tends to produce much more complicated patterns—which in the end may or may not have much to do with the constraint of densest packing.

One can look at all sorts of other physical systems, but so far as I can tell the story is always more or less the same: whenever there is behavior of significant complexity its most plausible explanation tends to be some explicit process of evolution, not the implicit satisfaction of constraints.

One might still suppose, however, that the situation could be different in biological systems, and that somehow the process of natural selection might produce forms that are successfully determined by the satisfaction of constraints.

But what I strongly believe, as I discuss in the next chapter, is that in the end, much as in physical systems, only rather simple forms can actually be obtained in this way, and that when more complex forms are seen they once again tend to be associated not with constraints but rather with the effects of explicit evolution rules—mostly those governing the growth of an individual organism.

Origins of Simple Behavior

There are many systems in nature that show highly complex behavior. But there are also many systems that show rather simple behavior—most often either complete uniformity, or repetition, or nesting.

And what we have found in this book is that programs are very much the same: some show highly complex behavior, while others show only rather simple behavior.

Traditional intuition might have made one assume that there must be a direct correspondence between the complexity of observed behavior and the complexity of underlying rules. But one of the central discoveries of this book is that in fact there is not.

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