Interactive demo
Interactive demo: cascade a sandpile
Click to drop grains, tune the rain, watch the power law emerge.
What the sequence shows
- An empty board, 4,096 cells, and sand falling at random. One rule only: at four grains a cell collapses and gives one to each of its four neighbours.
- Three thousand grains have fallen. Nothing, or nearly: the largest collapse moved three cells. The sand simply piles up.
- Six thousand grains, twice as high. Collapses appear at last — but tiny ones: twenty cells at most.
- The height stops at 2.1 grains per cell, and it will go no higher. Nobody chose that number: the pile found it on its own.
- One grain at a time now. More than one in two does nothing at all — then one of them, no different from the rest, collapses a quarter of the board.
- The points fall on a straight line. Which means: there is no typical avalanche. No size is more normal than any other.
- The biggest one we just saw is two hundred times the most common — same sand, same rule. Your turn: click to add a grain.
Controls
Estimated exponent τ:—
What you can try
- Drop the grains yourself — one click in two does nothing, one in thirty collapses a quarter of the board
- Turn the rain up full — the straight line draws itself in one second instead of ten
- Switch to the board of the real experiment, twice as wide — avalanches reach ten times higher, and the line keeps the same slope
Each button brings the pile to its critical point and changes a single setting — and stays a shareable link.