  Diffusion-driven patterns appear on curved surfaces in many settings,
initiated by unstable modes of an underlying Laplacian operator. On a flat
surface or perfect sphere, the patterns are degenerate, reflecting
translational/rotational symmetry. Deformations, e.g. by a bulge or
indentation, break symmetry and can pin a pattern. We adapt methods of
conformal mapping and perturbation theory to examine how curvature
inhomogeneities select and pin patterns, and confirm the results numerically.
The theory provides an analogy to quantum mechanics in a geometry-dependent
potential and yields intuitive implications for cell membranes, tissues, thin
films, and noise-induced quasipatterns.
