Tuesday, June 19, 2012

Turing Patterns and Animal Markings

Alan Turing is best known for the Turing Machine, breaking the Enigma-code and the Turing Test. Much less known is that he is one of the founders of mathematical biology, by writing in 1952 the article The chemical basis of morphogenesis

Because Turing knew nothing of genetics, scientists have long underestimated his one and only publication in mathematical biology. But the paper contains a load of interesting ideas and is on the transition point between the era of analytical mathematics and computational mathematics.

At the Turing Centenary conference How the World Computes mathematician Ian Stewart gave a public lecture this evening on Turing patterns and animal markings.

Here are some photo impressions with some quotes (click on the first one and you can go through all of them in larger format).

Ian Stewart: "If Turing would be alive today, he would be staggered where his theory on pattern formation has arrived."

Ian Stewart: "Patterns form by broken symmetries."

Ian Stewart: "Turing's reaction-diffusion equations show that local non-linearity combined with global diffusion create striking and often complex patterns."

Ian Stewart: "Theorem: A spotted animal can have a striped tail, but a striped animal cannot have a spotted tail."

And here are some stunning examples from patterns on shells from the Zoology Museum in Cambridge, next door to the conference:

This one has the pattern of a Sierpinski gasket:

Here are some more examples:

Later I will upload an MP3 audio recording of the lecture.

For the Dutch national newpaper NRC Handelsblad of Saturday June 23 I have written an article about Alan Turing's least known scientific contribution: mathematical biology, especially pattern formation.