  We investigate elementary cellular automata (ECA) from the point of view of
(discrete) dynamical systems. By studying small lattice sizes, we obtain the
complete phase space of all minimal ECA, and, starting from a maximal entropy
distribution (all configurations equiprobable), we show how the dynamics
affects this distribution. We then investigate how a vanishing noise alters
this phase space, connecting attractors and modifying the asymptotic
probability distribution. What is interesting is that this modification not
always goes in the sense of decreasing the entropy.
