相关论文: Fractal dimensions of the galaxy distribution vary…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
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…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
We present a review of the history and the present state of the fractal approach to the large-scale distribution of galaxies. Angular correlation function was used as a general instrument for the structure analysis. It was realized later…
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…
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…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
Using a sample of 133 991 galaxies distributed in the sky region $100^{\circ} <\alpha<270^{\circ}$ and $7^{\circ}<\delta<65^{\circ}$, extracted from the SDSS NASA/AMES Value Added Galaxy Catalog (AMES-VAGC), we estimate the fractal…
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…
We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D,…
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…
We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various…
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…
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…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
We discuss the problem of galaxy correlations by considering the various methods by which this information can be obtained. We focus in particular on the volume limited three dimensional samples and discuss a new way to increase the scale…