How does the zebra get its stripes? How does the leopard get its spots? And why should a mathematician be interested? In Alan Turing’s case, it was because this particular mathematician had an idea. And, as befits someone with a mind so thoroughly adapted to lateral thinking, the idea did not come from biology or mathematics – it came from chemistry.

Turing published his idea in 1952 ( It was simply that living cells may release chemicals that he called morphogens, which could diffuse gradually through a bundle of cells to affect their growth. The neat part was that, if another morphogen was coming from somewhere else in the bundle, the interaction between the two as they diffused could create patterns likes stripes and spots.

It was a brilliantly simple idea, and biologists are still exploring its ramifications. It was very similar to an idea that, unbeknown to Turing, the Russian chemists Anatol Zhabotinsky and Boris Belousov had been developing at around the same time – that a combination of reaction and diffusion could create patterns in a beaker full of chemicals.

The idea was so revolutionary that journal editors refused to accept their papers, saying that what they claimed was impossible ( But it wasn’t, as the picture above shows. To watch the process in action, have a look at a computer simulation (e.g. and marvel, just as chemists, biologists, and indeed mathematicians have been doing to this day.

IMAGE (Belousov-Zhabotinsky reaction in a Petri dish): Stephen Morris (chemistry by Michael Rogers)

(Zebra stripes); Wikimedia commons.

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