Smoothing a Rock by Chipping

Abstract

We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut from the object in a single chipping event. After many chips have been cut away, the resulting shape of the rock is generally anisotropic, with facet lengths and corner angles distributed over a broad range. Although a well-defined shape is quickly reached for each realization, there are large fluctuations between realizations.