Smooth pebbles on the beach are not spherical. They tend to be shaped more like oblate ellipsoids. But not axially symmetric. Obviously the population of shapes & sizes evolves as the water grinds them against each other. Is there one attractor-shape, or one at any given pebble-mass? Or can we understand the shape distribution? Here's a partial explanation. Spheres are unstable. If they get a bit oblate, then pebble will tend to lie on the flat side to lower its center of gravity, hence will grind itself flatter. But they don't get unboundedly flatter & flatter approaching a disc. Why not? Wear rate of surfaces (thickness loss per unit time) seems to be proportional to normal pressure times sliding speed. If the oblate does happen to tilt vertical, which will happen more often for disc like shapes, then get much higher pressure and probably also higher slide speed, which will grind it to become less oblate. So if it is too oblate it will evolve to be less so.