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This list can then be updated using
CCAEvolveStep[f_, list_List] := Map[f, (RotateLeft[list] + list + RotateRight[list])/3]
CCAEvolveList[f_, init_List, t_Integer] := NestList[CCAEvolveStep[f, #] &, init, t]
where for the rule on page 157 f is FractionalPart[3#/2] & while for the rule on page 158 it is FractionalPart[# + 1/4] & .
And while it is conceivable that this mapping may have some deep significance, none has so far ever been identified.
But while the first arrangement of colors shown below looks somewhat random, the last two are simple and purely repetitive.
And the problem is that while practical devices may eventually relax to what is essentially the same state, they can do this only at a certain rate.
And once again, at least for a while, any randomness in the motion of the ball can be attributed to randomness in this initial digit sequence.
As I will discuss in Chapter 10 , some of these methods have been well codified in standard mathematics and statistics, while others are effectively implicit in our processes of visual and other perception.
But while there are certainly mathematical equations that exhibit this phenomenon, none of those typically investigated have any close connection to realistic descriptions of fluid flow.
Thus, for example, the golden ratio spiral of branches on a plant stem can be viewed as a marvellous way to minimize the shading of leaves, while the elaborate patterns on certain mollusc shells can be viewed as marvellous ways to confuse the visual systems of supposed predators.
And indeed, while there are some traits—such as eye color and blood type in humans—that are more or less discrete, the vast majority of traits seen, say, in the breeding of plants and animals, show quite smooth variation.
But after a while it becomes clear what makes sense and what does not.