Grains
that
topple.
An Abelian sandpile, running live.
Threshold four. Boundaries fall away.
Every cell holds grains. Reach four and it topples, handing one grain to each neighbour — which may topple in turn. One grain too many and a single cell sets off an avalanche that repaints half the field.
Click anywhere on the field to place a grain.
Grains that topple off the edge are lost — that sink is what lets the pile balance itself.
Nobody tunes it. The pile finds the edge and stays there.
Four, then fall
A cell topples the instant it holds four grains. It sheds four — one to north, south, east, west — and its neighbours inherit the load. The order of toppling never changes the outcome; that is the Abelian in Abelian sandpile.
Avalanches of every size
Drip grains at random and the field organises itself. Most drops do nothing. A few trigger cascades that cross the whole plane. Plot the sizes and they trace a power law — the fingerprint of criticality, with no dial set to make it happen.
A fractal that is zero
Among all stable piles lives one that behaves like nothing — add it to any configuration and leave that configuration unchanged. Rendered, this identity element is an intricate self-similar fractal. Press Identity fractal to let a real avalanche paint it.