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underlying process. But the past several chapters have demonstrated that this is not only possible, but actually quite common.

Yet looking at the cellular automaton on the previous page there are clearly at least some regularities in the pattern it produces—like the diagonal stripes on the left. But if, say, one specifically picks out the color of the center cell on successive steps, then what one gets seems like a completely random sequence.

But just how random is this sequence really?

For our purposes here the most relevant point is that so far as one can tell the sequence is at least as random as sequences one gets from any of the phenomena in nature that we typically consider random.

When one says that something seems random, what one usually means in practice is that one cannot see any regularities in it. So when we say that a particular phenomenon in nature seems random, what we mean is that none of our standard methods of analysis have succeeded in finding regularities in it. To assess the randomness of a sequence produced by something like a cellular automaton, therefore, what we must do is to apply to it the same methods of analysis as we do to natural systems.

As I will discuss in Chapter 10, some of these methods have been well codified in standard mathematics and statistics, while others are effectively implicit in our processes of visual and other perception. But the remarkable fact is that none of these methods seem to reveal any real regularities whatsoever in the rule 30 cellular automaton sequence. And thus, so far as one can tell, this sequence is at least as random as anything we see in nature.

But is it truly random?

Over the past century or so, a variety of definitions of true randomness have been proposed. And according to most of these definitions, the sequence is indeed truly random. But there are a certain class of definitions which do not consider it truly random.

For these definitions are based on the notion of classifying as truly random only sequences which can never be generated by any simple procedure whatsoever. Yet starting with a simple initial condition and then applying a simple cellular automaton rule constitutes a simple

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