Self-erasing perturbations of Abelian sandpiles.

We investigate generalized seeding of the attracting states of Abelian sandpile automata and find there exists a class of global perturbations of such automata that are completely removed by the natural local dynamics. We derive a general form for such self-erasing perturbations and demonstrate that they can be highly nontrivial. This phenomenon provides a different conceptual framework for studying such automata and suggests possible applications for data protection and encryption.