Related papers: Fractal Approach to Large-Scale Galaxy Distributio…
The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies joined by filaments and walls, leaving large empty regions called cosmic voids. The most common method of describing the web is a…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
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…
It is known that the gas has a fractal structure in a wide range of spatial scales with a fractal dimension that seems to be a constant around Df = 2.7. It is expected that stars forming from this fractal medium exhibit similar fractal…
We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits…
We study the physical properties derived from interstellar cloud complexes having a fractal structure. We first generate fractal clouds with a given fractal dimension and associate each clump with a maximum in the resulting density field.…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
The statistical analysis and the spherical wavelet analysis of the SDSS DR7 quasars distribution and of the WMAP CMB anisotropy are performed. They revealed the qualitative agreement between the angular power spectrum of CMB and the angular…
Over the past two decades or so, it has become increasingly appparent that, out to quite large distances, galaxies are distributed in a quasi-fractal fashion with fractal dimension $D \approx 2$. Whether or not this behaviour continues onto…
We develop a field theoretical approach to the cold interstellar medium (ISM) and large structure of the universe. We show that a non-relativistic self- gravitating gas in thermal equilibrium with variable number of atoms or fragments is…
All the recent redshift surveys show highly irregular patterns of galaxies on scales of hundreds of megaparsecs such as chains, walls and cells. One of the most powerful catalog of galaxies is represented by the LEDA database that contains…
We measure the angular clustering of galaxies from the Sloan Digital Sky Survey Data Release 7 in order to probe the spatial distribution of satellite galaxies within their dark matter halos. Specifically, we measure the angular correlation…
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…
Several two-dimensional studies in spiral galaxies show that HII star formation regions have a fractal distribution, with a fractal dimension of approximately 2.3. In this work, the fractal dimension is calculated through the box-counting…
This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…
We perform a fractal analysis of the Southern Sky Redshift Survey 2, following the methods prescribed by Pietronero and collaborators, to check their claim that the galaxy distribution is fractal at all scales, and we discuss and explain…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the $2D$ fractal dimension $D$ of a cloud projected onto the sky plane. In…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…