  On the one hand, the large scale structure of matter is arguably scale
invariant, and, on the other hand, halos and voids are recognized as prominent
features of that structure. To unify both approaches, we propose to model the
dark matter distribution as a set of fractal distributions of halos of
different kinds. This model relies on the concept of multifractal as the most
general scaling distribution and on a plausible notion of halo as a singular
mass concentration in a multifractal. Voids arise as complementary to halos,
namely, as formed by regular mass depletions. To provide halos with definite
size and masses, we coarse-grain the dark matter distribution, using the length
given by the lower cutoff to scaling. This allows us to relate the halo mass
function to the multifractal spectrum. Hence, we find that a log-normal model
of the mass distribution nicely fits in this picture and, moreover, the
Press-Schechter mass function can be recovered as a bifractal limit.
  To support our model of fractal distributions of halos, we perform a
numerical study of the distribution produced in cosmological N-body
simulations. In the Virgo L-CDM GIF2 simulation, we indeed find fractal
distributions of halos with various dimensions and a halo mass function of
bifractal type. However, this mass function is not of Press-Schechter's type,
and we interprete it instead as caused by the undersampling of the distribution
at the scale of halos, due to discretization.
