But where does this complexity come from? We certainly did not put it into the system in any direct way when we set it up. For we just used a simple cellular automaton rule, and just started from a simple initial condition containing a single black cell.

Yet the picture shows that despite this, there is great complexity in the behavior that emerges. And indeed what we have seen here is a first example of an extremely general and fundamental phenomenon that is at the very core of the new kind of science that I develop in this book. Over and over again we will see the same kind of thing: that even though the underlying rules for a system are simple, and even though the system is started from simple initial conditions, the behavior that the system shows can nevertheless be highly complex. And I will argue that it is this basic phenomenon that is ultimately responsible for most of the complexity that we see in nature.

The next two pages [29, 30] show progressively more steps in the evolution of the rule 30 cellular automaton from the previous page. One might have thought that after maybe a thousand steps the behavior would eventually resolve into something simple. But the pictures on the next two pages [29, 30] show that nothing of the sort happens.

Some regularities can nevertheless be seen. On the left-hand side, for example, there are obvious diagonal bands. And dotted throughout there are various white triangles and other small structures. Yet given the simplicity of the underlying rule, one would expect vastly more regularities. And perhaps one might imagine that our failure to see any in the pictures on the next two pages [29, 30] is just a reflection of some kind of inadequacy in the human visual system.

But it turns out that even the most sophisticated mathematical and statistical methods of analysis seem to do no better. For example, one can look at the sequence of colors directly below the initial black cell. And in the first million steps in this sequence, for example, it never repeats, and indeed none of the tests I have ever done on it show any meaningful deviation at all from perfect randomness.

In a sense, however, there is a certain simplicity to such perfect randomness. For even though it may be impossible to predict what

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