Fractals and the Distribution of Galaxies
  This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications rather than their mathematical side. Then we discuss the standard correlation function analysis of galaxy catalogues and many observational facts that brought increasing doubts about the reliability of this method, paying special attention to the standard analysis implicit assumption of an eventual homogeneity of the distribution of galaxies. Some new statistical concepts for analysing this distribution is presented, and without the implicit assumption of homogeneity they bring support to the hypothesis that the distribution of galaxies does form a fractal system. The Pietronero-Wertz's single fractal (hierarchical) model is presented and discussed, together with the implications of this new approach for understanding galaxy clustering. 
Marcelo B. Ribeiro and Alexandre Y. Miguelote