But which specific cellular automaton rule will any given mollusc use? The pictures at the bottom of the facing page show all the possible symmetrical rules that involve two colors and nearest neighbors. And comparing the patterns in these pictures with patterns on actual mollusc shells, one notices the remarkable fact that the range of patterns that occur in the two cases is extremely similar.

Traditional ideas might have suggested that each kind of mollusc would carefully optimize the pattern on its shell so as to avoid predators or to attract mates or prey. But what I think is much more likely is that these patterns are instead generated by rules that are in effect chosen at random from among a collection of the simplest possibilities. And what this means is that insofar as complexity occurs in such patterns it is in a sense a coincidence. It is not that some elaborate mechanism has specially developed to produce it. Rather, it just arises as an inevitable consequence of the basic phenomenon discovered in this book that simple rules will often yield complex behavior.

And indeed it turns out that in many species of molluscs the patterns on their shells—both simple and complex—are completely hidden by an opaque skin throughout the life of the animal, and so presumably cannot possibly have been determined by any careful process of optimization or natural selection.

So what about pigmentation patterns on other kinds of animals? Mollusc shells are almost unique in having patterns that are built up one line at a time; much more common is for patterns to develop all at once all over a surface.

Most often what seems to happen is that at some point in the growth of an embryo, precursors of pigment-producing cells appear on its surface, and groups of these cells associated with pigments of different colors then become arranged in a definite pattern. Typically each individual group of cells is initially some fraction of a tenth of a millimeter across. But since different parts of an animal usually grow at different rates, the final pattern that one sees on an adult animal ends up being scaled differently in different places—so that, for example, the pattern is smaller in scale on the head of an animal, since the head grows more slowly.

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From Stephen Wolfram: A New Kind of Science [citation]