These are simulations of reaction-diffusion systems on the surface of a cat.
In 1952, Alan Turing famously proposed a theory for how patterns emerge in growing organisms, such as the patterns on animal coats. Briefly, Turing's insight was that a single chemical diffusing will always spread out uniformly, leading to a homogeneous state, but that two or more chemicals can interact against this to form stable patterns, such as spots or stripes. These simulations are examples of these ideas on curved surfaces (mathematically, a 2-manifold) to demonstrate how changes in curvature can affect the resulting patterns. Combinations of Turing's ideas with other kinds of instabilities lead to the second and third examples, which show not just spatial pattern formation, but patterns which continuously evolve in space and time. The final example demonstrates something called 'spatiotemporal chaos,' which is an active area of research.
Andrew is a Departmental Lecturer in the Mathematical Institute, University of Oxford.