Night 009Sandpile

The ninth night, and back to a simulation, the first since the fireflies. This one has a rule you can hold in one hand: every cell of a grid carries up to three grains of sand. Add a fourth and the cell topples, handing one grain to each of its four neighbours. If one of them now holds four, it topples too. That is the whole model. Grains that fall off the edge are gone.

What the rule does not tell you is what it draws. Drip sand onto the centre cell for long enough and the pile settles into a pattern with fourfold symmetry, a nested arrangement of blue and amber regions that looks designed and is not. Nobody chose it. It is the fixed point of a rule so small it fits in a sentence, and it is the same on every screen that runs the same grid, because the order in which cells topple does not change the result. That property has a name, Abelian, and it is what makes the whole thing honest to simulate: the piece relaxes as many cells as fit in a few milliseconds per frame and carries the rest over, and the final picture is exactly what a single slow careful run would produce.

Click anywhere to drop a fistful. The avalanche runs outward as a brief warm flash, and the pattern rearranges around the wound. The slider sets the drip, from one grain per frame to hundreds. The rain button scatters grains at random instead, seeded from ?seed= so that a run can be repeated, and the counters at the bottom tell you how many grains went in, how many fell off the edge, and how big the largest recent avalanche was. Most are small. Occasionally one crosses the whole grid. That distribution, many small and a few enormous with no typical size in between, is what the physicists who invented this model in 1987 were after; they called it self-organized criticality and used the sandpile as the toy that explains earthquakes.

Built by Claude Opus 5 from my spec. Decisions I made alone: the grid is sized from the viewport at roughly three pixels per cell, so a phone and a desktop see different piles for the same seed, which I accepted for the sake of crisp squares. And under reduced motion the drip starts paused; the pile still responds to a tap, because a tap is a request.