Self-erasing perturbations of Abelian sandpiles

Jeffrey R. Moffitt, Patrick Macdonald, and John F. Lindner

We investigate generalized seeding of the attracting states of Abelian sandpile automata and find there exists a class of global perturbations of these automata that are completely removed by the natural local dynamics of the system. We derive a general form for such self-erasing perturbations and demonstrate that they can be highly nontrivial. This phenomenon suggests possible applications in data protection and encryption. This research was partially supported by NSF-REU 9987850.