Cyclic cellular automata are two-dimensional cellular automata which generalize.
lattice versions of the Lorentz gas and certain biochemistry models of artificial
life. We show that rotators and time reversibility play a special role in the
creation of closed orbits in cyclic cellular automata. We also prove that almost
every orbit is closed (periodic) and the absence of diffusion for the flipping
rotator model (also known as the ant).