A Turing model for pattern generation on Lady beetles

Abstract: A Turing model for pattern generation on Lady beetles is considered. This motivates the construction of numerical algorithms for solving reaction-diffusion equations on the sphere. By applying a Galerkin approximation in space, and the implicit Euler method for timestepping, the equation is fully discretized. Convergence orders are proven for this scheme. To obtain a more efficient time stepping algorithm an implicit-explicit splitting is introduced. Some numerical experiments are then performed which demonstrates the superior efficiency of the splitting method. The experiments also verifies the pattern generating ability of the Turing model.