  New calculations to over ten million time steps have revealed a more complex
diffusive behavior than previously reported, of a point particle on a square
and triangular lattice randomly occupied by mirror or rotator scatterers. For
the square lattice fully occupied by mirrors where extended closed particle
orbits occur, anomalous diffusion was still found. However, for a not fully
occupied lattice the super diffusion, first noticed by Owczarek and Prellberg
for a particular concentration, obtains for all concentrations. For the square
lattice occupied by rotators and the triangular lattice occupied by mirrors or
rotators, 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 a
corresponding percolation problem. The questions arise therefore whether the
other critical points can be mapped onto a new percolation-like problem, and of
the dynamical significance of hyperscaling.
