  We systematically study the boundaries of one-dimensional, 2-color cellular
automata depending on 4 cells, begun from simple initial conditions. We
determine the exact growth rates of the boundaries that appear to be reducible.
Morphic words characterize the reducible boundaries. For boundaries that appear
to be irreducible, we apply curve-fitting techniques to compute an empirical
growth exponent and (in the case of linear growth) a growth rate. We find that
the random walk statistics of irreducible boundaries exhibit surprising
regularities and suggest that a threshold separates two classes. Finally, we
construct a cellular automaton whose growth exponent does not exist, showing
that a strict classification by exponent is not possible.
