But now that the results of this chapter are known, one can go back and see quite a number of times in the past when they came at least somewhat close to being discovered.

It turns out that two-dimensional versions of cellular automata were already considered in the early 1950s as possible idealized models for biological systems. But until my work in the 1980s the actual investigations of cellular automata that were done consisted mainly in constructions of rather complicated sets of rules that could be shown to lead to specific kinds of fairly simple behavior.

The question of whether complex behavior could occur in cellular automata was occasionally raised, but on the basis of intuition from engineering it was generally assumed that to get any substantial complexity, one would have to have very complicated underlying rules. And as a result, the idea of studying cellular automata with simple rules never surfaced, with the result that nothing like the experiments described in this chapter were ever done.

In other areas, however, systems that are effectively based on simple rules were quite often studied, and in fact complex behavior was sometimes seen. But without a framework to understand its significance, such behavior tended either to be ignored entirely or to be treated as some kind of curiosity of no particular fundamental significance.

Indeed, even very early in the history of traditional mathematics there were already signs of the basic phenomenon of complexity. One example known for well over two thousand years concerns the distribution of prime numbers (see page 132). The rules for generating primes are simple, yet their distribution seems in many respects random. But almost without exception mathematical work on primes has concentrated not on this randomness, but rather on proving the presence of various regularities in the distribution.

Another early sign of the phenomenon of complexity could have been seen in the digit sequence of a number like π ≃ 3.141592653… (see page 136). By the 1700s more than a hundred digits of π had been computed, and they appeared quite random. But this fact was treated essentially as a curiosity, and the idea never appears to have arisen that