Clustering paradigms and multifractal measures

Abstract

A subsample of the CfA galaxy catalog and two clustering models look different to the eye, yet have comparable two-point correlation functions. We show how the technique of "measure analysis" clearly reveals the nature of the differences, thereby providing an effective tool for discriminating between point set distributions. We present three clustering paradigms to assess this approach. As an illustration we use an explicitly calculable two-dimensional clustering model: the multiplicative multifractal. The three-dimensional models are a simple clustering hierarchy, and a clustering distribution consisting of the vertices of a three-dimensional Voronoi tessellation. Moreover, we analyze the CfA galaxy catalog in the same manner as our stochastic point processes.