English: The harmonic sandpile dynamics induced by some integer-valued harmonic function H on a finite convex domain (grid) of Z² are defined by

D(t)=(I-floor(t*dH))°. Thereby, I corresponds to the identity of the sandpile group on the domain, dH is the discrete Laplacian of H, (.)° is an operator mapping a given configuration to its respective recurrent configuration in the same equivalence class (corresponding to the relaxation operator if dH is non-positive), and t is a real variable (mod 1) interpreted as the time.

The animation shows the sandpile dynamics induced by the harmonic function H=x*y on a 255x255 square domain of Z². Thereby, x and y correspond to the standard coordinates of Z², with the origin assumed to lie in the center of the domain.

Black pixels correspond to vertices carrying zero grains of sand, green pixels to one grain, purple to two grains, and yellow to three grains.