Finite difference simulation of the wave equation on a sphere. There are Dirichlet boundary conditions on a discrete approximation of a Julia set, that has been scaled and then projected stereographically on a Riemann sphere, with the origin mapped to the north pole of the sphere. There are some artifacts at the north pole, due to the singularty of spherical coordinates.

In part 1, the colors and radial coordinate show the wave height. In part 2, they show the energy averaged over a time interval. The point of view rotates around the sphere in the course of the simulation.