FROM SMALL-SCALE FRACTALITY TO LARGE-SCALE HOMOGENEITY - A FAMILY OF CASCADING MODELS FOR THE DISTRIBUTION OF GALAXIES

We consider a class of fractal cascading models which describe the large-scale galaxy distribution. These fractal cascades are based on appropriate modifications of the beta-model which has been introduced in the study of turbulence. In particular, we consider a family of cascading processes which generate a scale-dependent fractal behavior and provide a smooth transition from small-scale fractality to large-scale homogeneity. In this context, the notion of "dressed" fractal dimension is introduced. The physical motivations for this approach are discussed in the framework of both cold- and hot-dark matter scenarios for galaxy formation.