A modified Allen-Cahn model for pattern synthesis on surfaces

Abstract: We propose an extension of the Allen-Cahn model for pattern synthesis on two dimensional curved surfaces. This model is based on a single PDE and it offers improved ability of controlling the type of generated surface patterns via the chosen reaction-diffusion coefficient, thus, obtaining patterns in form of spots, inverted spots, or stripes. We investigate the dependence of the type of the obtained pattern on the new proposed reaction term. An efficient operator splitting scheme is used to discretize the model on a surface. Experiments on surfaces with varying initial conditions illustrate a variety of patterns.