  If we treat the galaxies in published redshift catalogues as point sets, we
may determine the generalized dimensions of such sets by standard means,
outlined here. For galaxy separations up to about 5 Mpc, we find the dimensions
of the galaxy set to be about 1.2, with not a strong indication of
multifractality. For larger scales, out to about 30 Mpc, there is also good
scaling with a dimension of about 1.8. For even larger scales, the data seem
too sparse to be conclusive, but we find that the dimension is climbing as the
scales increase. We report simulations that suggest a rationalization of such
measurements, namely that in the intermediate range the scaling behavior is
dominated by flat structures (pancakes) and that the results on the smallest
scales are a reflection of the formation of density singularities.
