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And so as one example page 249 shows a two-dimensional cellular automaton often called the Game of Life in which all sorts of localized structures occur even on a white background.
Indeed, it is a general feature of class 4 cellular automata that with appropriate initial conditions they can mimic the behavior of all sorts of other systems.
So do all sufficiently large networks somehow correspond to ordinary space in a certain number of dimensions?
And at first I did not think of most of them as achieving any particular purposes at all.
Reading this book
This is a long book densely packed with ideas and results, and to read all of it carefully is a major undertaking.
Out of all possible Boolean functions the number that require BDDs of sizes 1, 2, ... is for n = 2 : {1, 0, 6, 9} and for n = 3 : {1, 0, 0, 27, 36, 132, 60} ; the absolute maximum grows roughly like 2 n .
From all these methods it is known that each kind of sensory input is first processed in its own specific area of the brain.
Venus, Mars, Europa (a moon of Jupiter) and Titan (a moon of Saturn) have for example all probably had liquid water at some time.
Analogously, one might imagine that it should be possible to have a function f[i, n] which enumerates all possible programs that always halt, and specifies a digit in their output when given input n .
Note that in all cases the size of the smallest representation must at some level increase like Log[m] (compare pages 1067 and 1070 ), but there may be some "algorithmically simple" integers that have shorter representations.