Chapter 8: Implications for Everyday Systems

Section 7: Biological Pigmentation Patterns

History [of shell patterns]

Elaborate patterns on shells have been noticed since antiquity, and have featured in a number of well-known works of art and literature. Since the late 1600s they have also been extensively used in classifying molluscs. But almost no efforts to understand the origins of such patterns seem to ever have been made. One study was done in 1969 by Conrad Waddington and Russell Cowe in which patterns on one particular kind of shell were reproduced by a specific computer simulation based on the idea of diverging waves of pigment. In 1982 I noticed that the patterns I had generated with 1D cellular automata looked remarkably similar to patterns on shells. I used this quite widely as an illustration of how cellular automata might be relevant to modelling natural systems. And I also made some efforts to do actual biological experiments, but I gave up when it seemed that the species of molluscs I wanted to study were difficult, if not impossible, to keep in captivity. Following my work, various other studies of shell patterns were done. Bard Ermentrout, John Campbell and George Oster constructed a model based on the idea that pigment-producing cells might act like nerve cells with a certain degree of memory. And Hans Meinhardt has constructed progressively more elaborate models based on reaction-diffusion equations.

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