Beating (cartoon) Heart

Fun Valentine's Day animation: An implicit "heart" surface is diffused forwards and backwards to simulate (cartoon) heart beating.

The implicit heart surface Phi=2-(2*X.^2 + Y.^2 + Z.^2 -1).^3 + 0.2*X.^2.*Z.^3 + Y.^2.*Z.^3 is diffused using the 3-D heat partial differential equation in a periodic box via the Fourier spectral method. After using fft's to handle the space derivatives, the remaining ordinary differential equation has an analytic solution in time. Once melted, the solution is run in reverse to simulate beating (this reversal part added by Luke Dosiek).