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instructions one can get all sorts of complex behavior is similar to the phenomenon we have seen in cellular automata.

But there is an important difference. For while the individual machine instructions executed by a computer may be quite simple, the sequence of such instructions defined by a program may be long and complicated. And indeed—much as in other areas of engineering—the typical experience in developing software is that to make a computer do something complicated requires setting up a program that is itself somehow correspondingly complicated.

In a system like a cellular automaton the underlying rules can be thought of as rough analogs of the machine instructions for a computer, while the initial conditions can be thought of as rough analogs of the program. Yet what we saw in the previous section is that in cellular automata not only can the underlying rules be simple, but the initial conditions can also be simple—consisting say of just a single black cell—and still the behavior that is produced can be highly complex.

So while practical computing gives a hint of part of what we saw in the previous section, the whole phenomenon is something much larger and stronger. And in a sense the most puzzling aspect of it is that it seems to involve getting something from nothing.

For the cellular automata we set up are by any measure simple to describe. Yet when we ran them we ended with patterns so complex that they seemed to defy any simple description at all.

And one might hope that it would be possible to call on some existing kind of intuition to understand such a fundamental phenomenon. But in fact there seems to be no branch of everyday experience that provides what is needed. And so we have no choice but to try to develop a whole new kind of intuition.

And the only reasonable way to do this is to expose ourselves to a large number of examples. We have seen so far only a few examples, all in cellular automata. But in the next few chapters [3, 4, 5, 6] we will see many more examples, both in cellular automata and in all sorts of other systems. And by absorbing these examples, one is in the end able to develop an intuition that makes the basic phenomena that I have discovered seem somehow almost obvious and inevitable.

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