  We consider a left permutive cellular automaton Phi, with no memory and
positive anticipation, defined on the space of all doubly infinite sequences
with entries from a finite alphabet. For each such automaton that is not
one-to-one, there is a dense set of points X (which is large in another sense
too) such that the Phi-orbit closure of each x in X is topologically conjugate
to an odometer (the ``+1'' map on a projective limit of finite cyclic groups).
We identify this odometer in several cases.

Dynamical Systems