Alan Turing and the mathematics of pattern formation in nature

> Not all biologists, however, have accepted this view. One of the strongest dissenters was D'Arcy Thompson (1917), who insisted that biological form is to be explained chiefly in the same way as inorganic form, i.e., as the result of physical and chemical processes. The primary task of the biologist is to discover the set of forms that are likely to appear. Only then is it worth asking which of them will be selected. Turing, who had been very much influenced by D'Arcy Thompson, set out to put the program into practice. Instead of asking why a certain arrangement of leaves is especially advantageous to a plant, he tried to show that it was a natural consequence of the process by which the leaves are produced. He did not in fact achieve his immediate aim, and indeed more than thirty-five years later the problem of phyllotaxis has still not been solved. On the other hand, the reaction-diffusion model has been applied to many other problems of pattern and form and Turing structures (as they are now called) have been observed experimentally (Castets at al. 1990), so Turing's idea had been vindicated.

Reading most of this introduction, especially this last paragraph, I couldn't but help think about Stephen Wolfram's A New Kind of Science. Wolfram's book is very empirically philosophical, or maybe I should say just purely explorational, and he goes into the problems described above almost word for word. He uses programs to demonstrate that, for example, the variation in patterns on shellfish is due to minimal changes in genetic programs.

[0] http://archive.is/VuXE7