Abelian sandpiles are grid-based systems where sand grains topple to neighboring cells when four or more accumulate in one spot. The toppling order doesn't matter (hence "abelian"), allowing sandpiles to be added together like numbers. Some patterns repeat (recurrent) while others don't (transient). The identity sandpile—a special configuration that leaves other sandpiles unchanged when combined—produces striking fractal-like geometric patterns with repeating triangular structures.
Sort: