Wave propagation, abelian property, identity element, sandpile group
Mode: Wave
Step: 0
Topplings: 0
Max chips: 0
Grid N:
Mode:
Speed: 5
The chip-firing game (Björner, Lovász, Shor 1991): each vertex holds integer chips; a vertex with ≥ deg(v) chips fires, sending one chip to each neighbor. Abelian property: the order of firings doesn't matter — the final stable configuration is unique. The set of stable configurations forms the sandpile group, a finite abelian group. The identity element has a fractal self-similar structure. Wave propagation shows toppling waves with 4-fold symmetry. Click to add chip bursts.