SUMS: Wormell -- The Mathematics of Biological Pattern Formation, or How the Leopard Got Its Spots

This week’s SUMS talk is by postgrad student John Wormell.  Pizza available afterwards! 

Abstract: 
Nature is full of stripes and spots: they are found on the plumage of all
sorts of plants and animals, in sand dunes, hair follicle distribution and even in
psychedelic hallucinations.  Often, these patterns are known to develop from homogeneous
embryonic conditions.  So what makes them form? 

Interestingly, this was something Alan Turing thought about.  He showed, in 1951, that
certain equations that govern many biological processes can develop a surprising
instability, allowing what we now call Turing patterns to arise seemingly out of
nothing.  His ideas have been since extended to all sorts of pattern-forming processes,
and have a lot to say about the kind of patterns that can form.  Turing patterns are key
in modern mathematical biology, and have been extended in all kinds of ways.  

In this talk we will go into the equations a little bit, and explain why Turing patterns
are so regular.  We’ll then talk about what this can tell us about patterns in nature,
making pretty pictures as we go.