  The automorphism group of a one dimensional shift space over a finite
alphabet exhibits different types of behavior: for a large class with positive
entropy, it contains a rich collection of subgroups, while for many shifts of
zero entropy, there are strong constraints on the automorphism group. We view
this from a different perspective, considering a single automorphism (and
sometimes endomorphism) and studying the naturally associated two dimensional
shift system. In particular, we describe the relation between nonexpansive
subspaces in this two dimensional system and dynamical properties of an
automorphism of the shift.
