Seminars

We survey the life of a Turing pattern, from initial diffusive instability through the emergence of dominant spatial modes and to an eventual spatially heterogeneous pattern. While many mathematically ideal Turing patterns are regular, repeating in structure and remaining of a fixed length scale throughout space, in the real world there is often a degree of irregularity to patterns. Viewing the life of a Turing pattern through the lens of spatial modes generated by the geometry of the bounded space domain housing the Turing system, we discuss how irregularity in a Turing pattern may arise over time due to specific features of this space domain or specific spatial dependencies of the reaction-diffusion system generating the pattern.

Everything you have been taught about Turing patterns is wrong! (Well, not everything, but qualifying statements tend to weaken a punchy first sentence). Turing patterns are universally used to generate and understand patterns across a wide range of biological phenomena. They are wonderful to work with from a theoretical, simulation and application point of view. However, they have a paradoxical problem of being too easy to produce generally, whilst simultaneously being heavily dependent on the details. In this talk I demonstrate how to fix known problems such as small parameter regions and sensitivity, but then highlight a new set of issues that arise from usually overlooked issues, such as boundary conditions, initial conditions, and domain shape. Although we’ve been exploring Turing’s theory for longer than I’ve been alive, there’s still life in the old (spotty) dog yet.