New calculations to over ten million time steps have revealed a more complexdiffusive behavior than previously reported, of a point particle on a squareand triangular lattice randomly occupied by mirror or rotator scatterers. Forthe square lattice fully occupied by mirrors where extended closed particleorbits occur, anomalous diffusion was still found. However, for a not fullyoccupied lattice the super diffusion, first noticed by Owczarek and Prellbergfor a particular concentration, obtains for all concentrations. For the squarelattice occupied by rotators and the triangular lattice occupied by mirrors orrotators, an absence of diffusion (trapping) was found for all concentrations,except on critical lines, where anomalous diffusion (extended closed orbits)occurs and hyperscaling holds for all closed orbits with {\em universal}exponents ${\displaystyle{d_f = \frac{7}{4}}}$ and ${\displaystyle{\tau =\frac{15}{7}}}$. Only one point on these critical lines can be related to acorresponding percolation problem. The questions arise therefore whether theother critical points can be mapped onto a new percolation-like problem, and ofthe dynamical significance of hyperscaling.
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