A family of sand automata

We study some dynamical properties of a family of two-dimensional cellular automata: those that arise from an underlying one-dimensional sand automaton whose local rule is obtained using a Latin square. We identify a simple sand automaton Γ whose local rule is algebraic, and classify this automaton as having equicontinuity points, but not being equicontinuous. We also show that it is not surjective. We generalise some of these results to a wider class of sand automata.