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But since essentially the only methods of analysis available were ones from traditional mathematics, very little of the complex behavior of typical biological systems was successfully captured.
The kinds of models that I introduce in this book involve no approximations when implemented on computers, and thus readily allow one to recognize much more complex phenomena.
One reason for this is that a region may break not into a simple line of smaller regions, but into concentric circles or into some collection of regions in a much more complicated arrangement—say of the kind that I discuss in the next section .
In the past one might have assumed that a system like this would be far too simple to correspond to our universe.
The picture below shows one example.
Thus for example the state of a substitution system at a particular step can be represented by the string ABBBABA , where the A 's correspond to white elements and the B 's to black ones.
Certainly it would be wonderful if one could just take the ideas and results in this book and somehow immediately use them to create models for all sorts of systems.
LFSR sequences
Often referred to as pseudonoise or PN sequences, maximal length linear feedback shift register sequences have repetition period 2 n - 1 and are generated by shift registers that go through all their possible states except the one consisting of all 0's, as discussed on page 974 .
The songs sometimes seem to be associated with attracting mates, and sometimes with defining territory—but often their function is unclear, even when one bird seems to sing in response to another.
But it was normally assumed that one should think only about explicit particles with realistic mechanical properties—so that abstract idealizations like cellular automata did not arise.