Pages 182 and 183 do however show a few examples of three-dimensional cellular automata. … And in particular, the basic phenomenon of complexity does not seem to depend in any crucial way on the dimensionality of the system one looks at.

Thus, for example, when we look at the behavior of a particular natural system, there will be certain features that we notice with our eyes, and certain features, perhaps different, that we can detect by doing various kinds of mathematical or other analysis. … Particularly when it comes to the higher levels of perception, there is much that we do not know for certain about this.

But to demonstrate that cyclic tag systems can manage to emulate cellular automata is not quite as straightforward as to do this for the various kinds of systems we have discussed so far. And indeed we will end up doing it in several stages.

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. … But there are a certain class of definitions which do not consider it truly random.

snowflakes come to have the intricate shapes they do. … And in fact in the course of this chapter , I will construct a whole sequence of remarkably simple models that do rather well at reproducing the main features of complex behavior in a wide range of everyday natural and other systems. … And certainly in each kind of system that I consider here there are many details that the models I discuss do not address.

And indeed I have tried hard to develop iterative search procedures that would do this. … So what does this mean for biological organisms? … When one does engineering, one normally operates under the constraint that the systems one builds must behave in a way that is readily predictable and understandable.

Indeed, the vast majority of animals do not tend to have overall forms that are dominated by any single kind of structure. … So how do all these parts get produced? … Usually there are some elements—such as bones—that eventually do become rigid.

For certainly a system like a typical cellular automaton does not—since for example its effective rules for evolution at different angles will usually be quite different. … But what was discovered around the end of the 1800s is that in the case of light it does not. … But now it turns out that the kinds of discrete causal network models that I have described almost inevitably end up being able to do this.

What does it ultimately involve? … Do these perhaps correspond to a higher-level type of human thinking? … And my strong suspicion is that when we do this we are in effect again just using memory, and retrieving patterns of logical argument that we have learned from experience.

There are certainly some tasks—such as playing chess or doing algebra—that at one time were considered indicative of human-like thinking, but which are now routinely done by computer. … No doubt part of the answer has to do with various practicalities of computers and storage systems. But a more important part, I suspect, has to do with issues of methodology.