Clustering paradigms and multifractal measures

A subsample of the CfA galaxy catalog and two clustering models look different to the eye, yet have comparable two-point correlation functions. It is shown how the technique of measure analysis clearly reveals the nature of the differences, thereby providing an effective tool for discriminating between point set distributions. Three clustering paradigms are presented to asses this approach. As an illustration, an explicitly calculable two-dimensional clustering model, the multiplicative multifractal, is used. The three-dimensional models are a simple clustering hierarchy, and a clustering distribution consisting of the vertices of a three-dimensional Voronoi tessellation. Moreover, the CfA galaxy catalog is analyzed in the same manner as the stochastic point processes. 53 refs.