Sandpile Identity Element

The abelian sandpile group on an n×n grid has an identity element — a configuration e such that e ⊕ e = e (where ⊕ is addition followed by stabilization). To find it: start with 6 everywhere, stabilize, subtract from 6 everywhere, stabilize again. The result is the fractal identity, exhibiting stunning self-similar structure tied to the group's algebraic properties.