Related papers: Are galaxy distributions scale invariant? A perspe…
The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
In the multi-fractal analysis of large scale matter distribution, the scale of transition to homogeneity is defined as the scale above which the fractal dimension of underlying point distribution is equal to the ambient dimension of the…
In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
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…
There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.
We characterize galaxy correlations in the Sloan Digital Sky Survey by measuring several moments of galaxy counts in spheres. We firstly find that the average counts grows as a power-law function of the distance with an exponent D= 2.1+-…
Extensive confusion exists and persists in the literature on dynamical systems theory, cosmology, and other fields over spectra of fractal dimensions. Entirely different generating functions have been treated as if they should yield…