How the zebra (might have) got its stripes: Realistic pattern formation with curvature-dependent reaction-diffusion models

Synopsis

Many animals and plants have distinctive visual patterns (like stripes or spots) that they use for camouflage or to stand out in their environment. Often, the patterns are remarkably consistent between individuals within a species. How do these patterns form so accurately? More specifically, how does a particular hair follicle on a zebra “know” to produce a black hair, while its neighbor produces a white hair? We should be able to describe these patterns with rules derived from biophysical principles like the organism’s geometry and gene-protein interactions. In this presentation, I’ll give an introduction to how a class of simple models (reaction-diffusion/Turing models) can lead to pattern formation, then extend to curvature-dependent diffusion and analyze the model’s success in reproducing real-world patterns on animals like zebras and cats.