Initial conditions for typical portions of the Universe are studied. Using the kinematic Zeldovich approximation we set the primeval density perturbations corresponding to the standard random phase Cold Dark Matter scenario (CDM). In the CDM models we verify that it is necessary to bias the galaxy distribution with respect to the mass distribution in order to satisfy simultaneously the amplitude and power of the spatial two point correlation function. It is seen the difference between these distributions, where the "galaxy" distribution was obtained by a prescription that assigns galaxies only to those particles that have more than a certain number of neighbors on a given scale (3 Mpc). This procedure is equivalent to the assumption of the existence of astrophysical mechanisms that induced galaxy formation. The mass and "galaxy" two point functions are power laws differing only their amplitudes. We note that the simulated galaxy distribution has similar properties than the observations. We are presently studying the implementation of statistical methods that say provide useful information concerning the filamentary structure in both observations and simulations. The techniques being studied may provide important information and permit characterizations of models and observations where the usual n-point functions give partial information.