Title: Cellular automata connections,
Abstract: It is shown that any two cellular automata (CA) in rule space can be
connected by a continuous path parameterized by a real number $\kappa \in (0,
\infty)$, each point in the path corresponding to a coupled map lattice (CML).
In the limits $\kappa \to 0$ and $\kappa \to \infty$ the CML becomes each of
the two CA entering in the connection. A mean-field, reduced model is obtained
from the connection and allows to gain insight in those parameter regimes at
intermediate $\kappa$ where the dynamics is approximately homogeneous within
each neighborhood.