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We develop a method of multifractal analysis of N-body cosmologicalsimulations that improves on the customary counts-in-cells method by takingspecial care of the effects of discreteness and large scale homogeneity. Theanalysis of the Mare-Nostrum simulation with our method provides strongevidence 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-lawexponent -2, as corresponds to a multifractal. Furthermore, our analysis showsthat the dark matter and gas distributions are indistinguishable asmultifractals. To determine if there is any gas biasing, we calculate thecross-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, upto the scale of homogeneity. However, entropic measures related to the Bayesiananalysis show that this gas bias is small (in a precise sense) and is such thatthe fractal singularities of both distributions coincide and are identical. Weconclude that this common multifractal cosmic web structure is determined bythe dynamics and is independent of the initial conditions.

Fractal distributions of dark matter and gas in the MareNostrum Universe