Chapter 8: Implications for Everyday Systems

Section 7: Biological Pigmentation Patterns

Examples [of reaction-diffusion] in chemistry

Overall concentrations in chemical reactions can be described by nonlinear ordinary differential equations. Reactions with oscillatory behavior were predicted by Alfred Lotka in 1910 and observed experimentally by William Bray in 1917, but for some reason they were not further investigated at that time. An example was found experimentally by Boris Belousov in 1951 and extensive investigations of it were begun by Anatol Zhabotinsky around 1960. In the early 1970s spiral waves were seen in the spatial distribution of concentrations in this reaction, and by the end of the 1970s images of such waves were commonly used as icons of the somewhat ill-defined notion of self-organization.

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