Sand automata as cellular automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with simple sand automata. We show that the classical definition of nilpotency is not meaningful for sand automata. Then, we introduce the suitable new notion of flattening sand automata. Finally, we prove that this simple dynamical behavior is undecidable.