But the crucial point that was missed is that computers are not just limited to working out consequences of mathematical equations. And indeed, what we have seen in this chapter is that there are fundamental discoveries that can be made if one just studies directly the behavior of even some of the very simplest computer programs.

In retrospect it is perhaps ironic that the idea of using simple programs as models for natural systems did not surface in the early days of computing. For systems like cellular automata would have been immensely easier to handle on early computers than mathematical equations were. But the issue was that computer time was an expensive commodity, and so it was not thought worth taking the risk of trying anything but well-established mathematical models.

By the end of the 1970s, however, the situation had changed, and large amounts of computer time were becoming readily available. And this is what allowed me in 1981 to begin my experiments on cellular automata.

There is, as I mentioned above, nothing in principle that requires one to use a computer to study cellular automata. But as a practical matter, it is difficult to imagine that anyone in modern times would have the patience to generate many pictures of cellular automata by hand. For it takes roughly an hour to make the picture on page 27 by hand, and it would take a few weeks to make the picture on page 29.

Yet even with early mainframe computers, the data for these pictures could have been generated in a matter of a few seconds and a few minutes respectively. But the point is that one would be very unlikely to discover the kinds of fundamental phenomena discussed in this chapter just by looking at one or two pictures. And indeed for me to do it certainly took carrying out quite large-scale computer experiments on a considerable number of different cellular automata.

If one already has a clear idea about the basic features of a particular phenomenon, then one can often get more details by doing fairly specific experiments. But in my experience the only way to find phenomena that one does not already know exist is to do very systematic and general experiments, and then to look at the results with as few preconceptions as possible. And while it takes only rather basic