Surface Toppling on Cylindrical and Polyhedral Sandpiles
Benjamin R. Trube

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 105–112
Regular Papers

Abstract

Abelian Sandpiles are commonly investigated on unbounded two-dimensional square lattices. Less explored is the behavior of sandpiles on three-dimensional surfaces. In this paper I investigate partially and fully closed sandpile graphs that can be wrapped around cylinders and cubes. Aside from attractive symmetries not possible on a uniform flat lattice, I am interested in the ways that bending the sandpile in on itself this way can produce novel interactions. I study how the quantity and placement of drop spots affected the final stabilized pattern aesthetically and the density of sand throughout the sandpile.

Files