The slope that never finishes settling

Grains fall on the left. Each column holds until it is a little steeper than the one below it can bear, and then it sheds one grain downhill — which may be all that happens, or may be the first move of a slide that runs the length of the slope. You are not steering any of this. You dropped a grain; the pile decided the rest.

What the tally is looking for is a favourite size, and there isn’t one. Each row covers twice the span of the row above it, and the bars step down evenly with no bump anywhere: one-column slips and slope-wide collapses come out of the same heap under the same rule, and nothing about the grain you just dropped says which you are about to get. The last row piles up only because a slide cannot run further than the pile is long.

So the heap is not settling toward a stable angle and stopping. It settles to the angle at which it is just barely failing everywhere at once, and then stays there, permanently about to slide. That state is the resting state.

Switch to round grain and it becomes a different object. Now every column tips at exactly the same steepness, the surface pulls straight, and every slide is the same slide — the whole slope, every time. There is a typical avalanche; it is the only one. The rumpled pile is the one with no typical anything.

That difference is not only a modelling convenience. In 1996 a group in Oslo poured rice between two sheets of glass and photographed the slides, and found that long, thin grains gave avalanches of every size while rounder grains did not. The shape of the grain decides whether the pile has a favourite way to fail.