Growing sandpiles: A model of Proportionate Growth
Adding sand grains at a single site in the Abelian sandpile models on an initailly periodic background configuration produces beautiful but complex patterns. These show the very interesting property of proportionate growth, familiar in biology, where different parts of the growing animal grow at roughly the same rate. We will discuss a special case where the resulting pattern can be characterized in detail. The relationship to more general problem of approximating a function by piecewise-linear or -quadratic approximants will be discussed. We also discuss changes in the patterns produced near absorbing boundaries.