We investigate the dynamical behavior arising from a coupled model of bulk diffusion and surface reaction. For the 2D case, implementation of the closest point method suggests the existence of Turing patterns for equal diffusion coefficients.

A deterministic model may sometimes seem to be a good description of the dynamics of an observed system but may have a long-term stable constant limit, whereas observations of the system itself show a noisy pattern. An example is semi-arid vegetation patterns. Adding noise to the model may well reveal the pattern. In this talk I show some photos, talk about some math, and show some simulations. This is not a magic show.