The life of a Turing Pattern

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.