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Most present-day mechanical devices, for example, are built only for rather specific tasks, and are not universal.
But presumably one will actually find examples much earlier—since for example the 2-state 3-color machine on page 709 is only number 596,440.
And if one thinks only about this idealization one almost inevitably concludes that the system has very little computational sophistication.
And for example its whole idea of using mathematical formulas to describe behavior makes sense only when the behavior is computationally reducible.
Despite the fact that mobile automata update only one cell at a time, it is thus still possible for them to produce behavior of great complexity.
If one looks at recent work in number theory, most of it tends to be based on rather sophisticated methods that do not obviously depend only on the normal axioms of arithmetic.
But whereas in physics one has only to look at the natural world to see that other more complex phenomena exist, the usual approaches to mathematics provide almost no hint of anything analogous.
Rule (c) was found by a large search, and involves only 3 colors.
Indeed, away from the right-hand edge, all the elements effectively behave as if they were lying on a regular grid, with the color of each element depending only on the previous color of that element and the element immediately to its right.
But with the new kinds of models based on simple programs that I explore in this book it becomes possible to capture all sorts of much more complex features that can only really be seen in explicit images of behavior.