  Let $X=S^G$ where $G$ is a countable group and $S$ is a finite set. A
cellular automaton (CA) is an endomorphism $T : X \to X$ (continuous, commuting
with the action of $G$). Shereshevsky (1993) proved that for $G=Z^d$ with $d>1$
no CA can be forward expansive, raising the following conjecture: For $G=Z^d$,
$d>1$ the topological entropy of any CA is either zero or infinite. Morris and
Ward (1998), proved this for linear CA's, leaving the original conjecture open.
We show that this conjecture is false, proving that for any $d$ there exist a
$d$-dimensional CA with finite, nonzero topological entropy. We also discuss a
measure-theoretic counterpart of this question for measure-preserving CA's. Our
main tool is a construction of a CA by Kari (1994).
