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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 observational limits. The value of the fractal dimension(s) calculated by different authors have become the object of a large debate, as have been the value of the expected transition from fractality to a possible large scale homogeneity. Moreover, some authors have proposed that different scaling regimes might be discerned at different lenght scales. To go further on into this issue, we have applied the correlation integral method to the wider sample currently available. We therefore obtain a fractal dimension of the galaxy distribution which seems to vary by steps whose width might be related to the organization hierarchy observed for the galaxies. This result could explain some of the previous results obtained by other authors from the analyses of less complete catalogs and maybe reconcile their apparent discrepancy. However, the method applied here needs to be further checked, since it produces odd fluctuations at each transition scale, which need to be thoroughly explained.
We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {em one} disordered system experience strong level-to-level fluctuations in a
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of homogeneity. In thi
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 that a norma
Annotations in Visual Analytics (VA) have become a common means to support the analysis by integrating additional information into the VA system. That additional information often depends on the current process step in the visual analysis. For exampl
The theory of zeta functions of fractal strings has been initiated by the first author in the early 1990s, and developed jointly with his collaborators during almost two decades of intensive research in numerous articles and several monographs. In 20