  We develop a method of multifractal analysis of N-body cosmological
simulations that improves on the customary counts-in-cells method by taking
special care of the effects of discreteness and large scale homogeneity. The
analysis of the Mare-Nostrum simulation with our method provides strong
evidence of self-similar multifractal distributions of dark matter and gas,
with a halo mass function that is of Press-Schechter type but has a power-law
exponent -2, as corresponds to a multifractal. Furthermore, our analysis shows
that the dark matter and gas distributions are indistinguishable as
multifractals. To determine if there is any gas biasing, we calculate the
cross-correlation coefficient, with negative but inconclusive results. Hence,
we develop an effective Bayesian analysis connected with information theory,
which clearly demonstrates that the gas is biased in a long range of scales, up
to the scale of homogeneity. However, entropic measures related to the Bayesian
analysis show that this gas bias is small (in a precise sense) and is such that
the fractal singularities of both distributions coincide and are identical. We
conclude that this common multifractal cosmic web structure is determined by
the dynamics and is independent of the initial conditions.
