  In this paper we review previous work and present new work concerning the
relationship between dynamical systems theory and computation. In particular,
we review work by Langton \cite{Langton90} and Packard \cite{Packard88} on the
relationship between dynamical behavior and computational capability in
cellular automata (CA). We present results from an experiment similar to the
one described in \cite{Packard88}, that was cited there as evidence for the
hypothesis that rules capable of performing complex computations are most
likely to be found at a phase transition between ordered and chaotic behavioral
regimes for CA (the ``edge of chaos''). Our experiment produced very different
results from the original experiment, and we suggest that the interpretation of
the original results is not correct. We conclude by discussing general issues
related to dynamics, computation, and the ``edge of chaos'' in cellular
automata.
