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The reason I chose this kind of network in Chapter 5 is that there happens to be a fairly easy way to set up evolution rules for such networks.
And for the particular mobile automaton rule used here, the network one gets ends up being highly regular, as illustrated in pictures (h) and (i).
But if one has a system that yields the same causal network independent of the scheme used to apply its underlying rules, then the situation is different.
Nevertheless, a potentially important point is that it is in some ways misleading to think of particles in a network as just interacting according to some definite rule, and being perturbed by what is in essence a random background.
As I mentioned above, ordinary quantum processes can appear to follow different histories depending on what scheme is used to decide the order in which underlying rules are applied.
And thus, for example, having myself seen thousands of pictures produced by cellular automata, I can recognize immediately from memory almost any pattern generated by any of the elementary rules—even though none of the other methods of perception and analysis can get very far whenever such patterns are at all complex.
In fact, this is the essence of the very general phenomenon of attractors that we discussed in Chapter 6 —and it is seen in the vast majority of cellular automata, and in fact in almost any kind of system that follows definite rules.
But it should be emphasized that among systems of any particular type—say cellular automata—not all possible underlying rules are capable of supporting the same kinds of computations.
There are then a few terms that specify the particular initial conditions used here, followed by terms that give the rule for the Turing machine that is used.
And indeed for example traditional mathematics has for the most part never even considered most of the kinds of systems that I discuss in this book—even though they are based on some of the very simplest rules possible.