Nematic Chainmail and the Abelian Sandpile Model

We show that topological classes of nonsingular solitons entangled with a weaved array of fixed nematic defects are in correspondence with stable recurrent states of the Abelian sandpile model. The physical correspondence is made by identifying a local Skyrmion flux with sandpile height. Using a toy model of these topological states, we discuss properties of large systems.