NEW RESULTS FOR DIFFUSION IN LORENTZ LATTICE-GAS CELLULAR-AUTOMATA

New calculations to over ten million time steps have revealed a more c omplex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rot ator scatterers. For the square lattice fully occupied by mirrors wher e extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration , obtains for all concentrations. For the square lattice occupied by r otators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, exc ept on critical lines, where anomalous diffusion (extended closed orbi ts) occurs and hyperscaling holds for all closed orbits with universal exponents d(f)=7/4 and tau=15/7. Only one point on these critical lin es can be related to a corresponding percolation problem. The question s arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of h yperscaling.