Fast Simulation of Laplacian Growth

Laplacian instability is the physical mechanism driving pattern formation in many disparate natural phenomena. Current algorithms for simulating this instability are slow and memory intensive. A new algorithm, based on the dielectric breakdown model from physics, is more than three orders of magnitude faster than previous methods and decreases memory use by two orders of magnitude. Our algorithm admits a spherical harmonic solution, letting it account for arbitrary boundary data, such as an environment map