I will discuss joint work with Lionel Levine and Wesley Pegden. The Abelian sand pile is a deterministic diffusion process on graphs originally designed to model self-organized criticality. On periodic graphs, the sandpile generates approximations of striking fractal images. Our work identifies the scaling limit of the sandpile. The algebraic character of the limit explains the appearance of the fractal images. Our methods involve a mixture of pure mathematics and computational exploration.