This simulation shows a solution to the wave equation in spherical geometry. The initial condition is an approximation of a Dirac delta mass at the North Pole in terms of the first 25 spherical harmonics. From there, the wave propogates southward before collapsing on itself at the South Pole and returning to the north.
Whenever you compute the Fourier coefficients for a discontinuous signal, there are peaks and valleys from the fact that the partial sum of trigonometric polynomials cannot converge uniformly. This is known as Gibbs phenomena, and the same exact thing happens with spherical harmonics. The shading highlights the peaks and valleys on the surface, which is why they appear as a...