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And certainly if this example is anything to go by, it begins to seem unlikely that the more complex kinds of patterns that we have seen so many times in this book could ever realistically be represented by such formulas.
But just as it is difficult to make an analog computer faithfully reproduce many steps in a discrete computation, so also it seems likely that it will be difficult to set up differential equations that for arbitrarily long times successfully manage to emulate the precise behavior of systems like cellular automata.
But in recent times it has usually been assumed that it has something to do with an ability to perform sophisticated computations.
Presumably the reason—as I have mentioned several times in this book—is that its whole methodology has tended to be based on setting up systems whose behavior is simple enough that almost every aspect of them can always readily be predicted.
History [of multiway systems]
Versions of multiway systems have been invented many times in a variety of contexts.
The basic argument for Kolmogorov's k -5/3 result for the spectrum of turbulence is independent of dimension, but there are reasons to believe that in 2D eddies will tend to combine, so that after sufficiently long times only a small number of large eddies will be left.
History [of continuous cellular automata]
Continuous cellular automata have been introduced independently several times, under several different names.
Following work by Kirill Sitnikov in 1960 and by Vladimir Alekseev in 1968, it was established that with suitably chosen initial conditions, the equation yields any sequence Floor[t[i + 1] - t[i]] of successive zero-crossing times t[i] .
History of embryology
General issues of embryology were already discussed in Greek times, notably by Hippocrates and Aristotle .
But countless times I have been asked how models based on simple programs can possibly be correct, since even though they may successfully reproduce the behavior of some system, one can plainly see that the system itself does not, for example, actually consist of discrete cells that, say, follow the rules of a cellular automaton.