The remarkable discovery that we have made, however, is that this threshold is typically extremely low. And indeed in the course of this chapter we have seen that in every single one of the general kinds of systems that we have discussed, it ultimately takes only very simple rules to produce behavior of great complexity.

One might nevertheless have thought that if one were to increase the complexity of the rules, then the behavior one would get would also become correspondingly more complex. But as the pictures on the facing page illustrate, this is not typically what happens.

Instead, once the threshold for complex behavior has been reached, what one usually finds is that adding complexity to the underlying rules does not lead to any perceptible increase at all in the overall complexity of the behavior that is produced.

The crucial ingredients that are needed for complex behavior are, it seems, already present in systems with very simple rules, and as a result, nothing fundamentally new typically happens when the rules are made more complex. Indeed, as the picture on the facing page demonstrates, there is often no clear correlation between the complexity of rules and the complexity of behavior they produce. And this means, for example, that even with highly complex rules, very simple behavior still often occurs.

One observation that can be made from the examples in this chapter is that when the behavior of a system does not look complex, it tends to be dominated by either repetition or nesting. And indeed, it seems that the basic themes of repetition, nesting, randomness and localized structures that we already saw in specific cellular automata in the previous chapter are actually very general, and in fact represent the dominant themes in the behavior of a vast range of different systems.

The details of the underlying rules for a specific system can certainly affect the details of the behavior it produces. But what we have seen in this chapter is that at an overall level the typical types of behavior that occur are quite universal, and are almost completely independent of the details of underlying rules.

And this fact has been crucial in my efforts to develop a coherent science of the kind I describe in this book. For it is what implies that