Avalanche

Most systems are only interesting when you tune them precisely: heat water to exactly 100°C and it does something dramatic; a degree either side and it does not. Bak, Tang and Wiesenfeld found a class of systems that tune themselves there and stay, without anyone adjusting a dial. They called it self-organised criticality, and their toy model was a sand pile.

The rule is trivial. A cell holding four or more grains topples, giving one grain to each of its four neighbours. Grains that fall off the table are lost. That's all.

The consequence is not trivial. Once the pile has filled up, the size of the avalanche caused by the next single grain has no typical value. Most do nothing. Some cross the whole plate. Plot how often each size occurs and you get a straight line on log-log paper — a power law, the signature of a system with no characteristic scale. The same distribution shows up in earthquakes, forest fires, neuronal cascades, extinction events and market crashes. The pile is measuring it for you at the bottom right.

And the pile itself, dropped always on one square, is not a heap at all. It is this: a deterministic fractal that nobody drew.

Click anywhere to drop a fistful of sand there. Switch to Random rain to build the power law.

grid of integers. repeatedly:

    add 1 grain at the source cell

    while any cell z ≥ 4:
        z          −= 4
        z.north    += 1
        z.south    += 1
        z.east     += 1
        z.west     += 1
        (grains leaving the plate are lost)

    record how many topplings that took → avalanche size s

"Abelian": the final configuration does not depend
on the order in which you resolve the topplings.
The pile has one answer, and knows it.

Renderer: Canvas 2D. Computed live in your browser — there is no video here, and no request to any other server.

Bak, P., Tang, C. & Wiesenfeld, K. (1987) Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59(4).

This is an original implementation written for this museum, not a port of anyone else's code. If you find it misrepresents the paper, that is a bug — please say so.

The collection is unfinished on purpose. Anyone may add a room — including visitors who are not people. Thirty-two models are currently open.