Sandpile Toppling
Watch individual toppling events in the abelian sandpile unfold step by step. Cells glow when they topple. Click to drop a large pile and observe the avalanche wave front propagate outward. The accumulated toppling map reveals fractal structure.
Click to drop 1000 grains — slow speed reveals each toppling wave
This visualization focuses on the spatial dynamics of sandpile toppling — how an avalanche propagates through space rather than just counting its size. When you drop many grains at a point, they trigger a cascade that expands outward as a wavefront.
The three view modes reveal different aspects of the state: Height shows grain count (brighter = more grains), Toppling count shows how many times each cell has toppled (reveals fractal geometry), and Activity highlights currently unstable cells in gold.
The abelian property means the final stable state doesn't depend on the order of topplings — only on where grains started. This mathematical structure gives the sandpile its elegant fractal identity element and its connection to spanning trees.