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The idea is that when a pattern forms, the color of each element will tend to be the same as the average color of nearby elements, and opposite to the average color of elements further away.
Yet despite this, my discoveries about cellular automata still involved a substantial element of luck.
Yet just as it seems unreasonable to imagine that the universe consists of a rigid grid of cells in space, so also it seems unreasonable to imagine that there is a global clock which defines the updating of every element in the universe synchronized in time.
Picture (b) then shows another version of this same evolution, but now rearranged so that each element stays in the same position, rather than always shifting to the left at each step.
But as the pictures on the facing page and in Chapter 10 illustrate, if one allows more general kinds of underlying rules then it becomes quite straightforward to set up procedures that with very little computational effort can find the color of any element in any nested pattern.
But it is extremely common in all sorts of natural systems to see effects that propagate from one element to another.
For typically it operates by building systems up in such a way that the behavior of each element can always readily be predicted by something like a simple mathematical formula.
If exactly m + 1 distinct blocks occur for every m , then the sequence must be of the so-called Sturmian type discussed on page 916 , and the n th element must be given by Round[(n + 1) a + b] - Round[n a + b] , where a is an irrational number.
Animism is also a key element of the New Age movement of the 1960s, as well as of such ideas as the Gaia Hypothesis.
One simple approach illustrated below is to consider a sequence of elements produced by the system, and then to take each element to correspond to a vibration for a brief time—say a thousandth of a second—in one of two directions.