Fractals and the Distribution of Galaxies

Ribeiro, Marcelo B.; Miguelote, Alexandre Y.

doi:10.1590/s0103-97331998000200007

Cited by 41 publications

(30 citation statements)

References 22 publications

(55 reference statements)

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“…The controversy started with Pietronero's (1987) claims that the usual correlation statistics employed in the characterization of the distribution of galaxies cannot be applied to this distribution, and that a novel statistical technique proposed by him is capable of testing, rather than assuming, whether or not the galaxy distribution is uniform. 5 The main results reached by this side of the debate are the absence of any sign of homogenization of the distribution of galaxies up to the limits of current observations, denying, thus, any usefulness to a correlation length concept (see §1 above), and that this distribution is well described as forming a single fractal structure, with dimension D ≈ 2 (Coleman and Pietronero 1992;Pietronero et al 1997;Ribeiro and Miguelote 1998;SylosLabini et al 1998;Pietronero and Sylos-Labini 2000).…”

Section: The Fractal Debatementioning

confidence: 99%

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

Ribeiro¹

2001

General Relativity and Gravitation

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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, and conjecturing that this distribution should follow a fractal pattern, in the sense of having a power-law type average density profile, in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts by reviewing the argument concerning the possibility that the galaxy distribution follows such a scale invariant pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that in order to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ∼ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist. John Maynard Keynes (1936)

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Section: The Fractal Debatementioning

confidence: 99%

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

Ribeiro¹

2001

General Relativity and Gravitation

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“…In limit → 0, the measure L becomes asymptotically equal to the length of the real curve and is independent of (Ribeiro and Miguelote, 1998).…”

Section: Point Density and Point Spacingmentioning

confidence: 99%

Point Distribution as True Quality of LiDAR Point Cloud

Kodors¹

2017

BJMC

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Abstract.A parameter "point density" is often used to evaluate the quality of aerial laser scanning data. It is a parameter simple for understanding and human imagination. However, the true quality of LiDAR point cloud is based on point distribution. There are researches, which mention importance of point distribution and users' false perception, that higher point density is better quality of LiDAR point cloud. The goal of this study is to define the mathematical model how to measure quality of LiDAR point cloud. This article discusses the point distribution and LiDAR data quality defining the image resolution of point cloud. It can be interesting for experts in civil geospatial intelligence, LiDAR data processing and flight planning.

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“…Since, these two quantities are fundamental in the characterization of a single fractal structure (Ribeiro and Miguelote 1998), they can also be expected to be equally fundamental in the fractal characterization of the perturbed model considered here.…”

Section: Observational Relations Along the Past Null Conementioning

confidence: 99%

“…While Ribeiro (1992b) showed that an unperturbed EdS model does not have scale invariant features, in the sense of not having a power law decay of the average density at increasing depths, it, nevertheless, also showed very clearly that there is indeed a strong decay of the average density at increasing values of the luminosity distance or the redshift, an effect termed by Ribeiro (1995) as "observational inhomogeneity of the standard model". 2 Bearing this result in mind, it is only natural to ask whether or not a perturbed model could turn the density decay at increasing redshift depths into a power law type decay, as predicted, and claimed to be observed, by the scale invariant description of galaxy clustering (Pietronero 1987;Coleman and Pietronero 1992;Pietronero et al 1997;Ribeiro and Miguelote 1998;Sylos-Labini et al 1998;Pietronero and Sylos-Labini 2000).…”

Section: Introductionmentioning

confidence: 96%

“…Unaware of Wertz's work, but inspired by de Vaucouleurs, Mandelbrot (1983) revived the hierarchical universe model and made a thorough discussion about the scaling properties of galaxy distribution, fully characterizing it as a scale invariant structure. A discussion about the similarities and differences between Wertz's and Pietronero's approaches to the problem of universal hierarchical clumping of matter can be found in Ribeiro and Miguelote (1998;see also Ribeiro 1994).…”

Section: Introductionmentioning

confidence: 99%

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Scale Invariance in a Perturbed Einstein-De Sitter Cosmology

Abdalla

Mohayaee

Ribeiro³

2001

Fractals

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This paper seeks to check the validity of the apparent fractal conjecture (Ribeiro 2001ab), which states that the observed power-law behaviour for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone.Since general relativity states that astronomical observations are carried out in this spacetime hypersurface, observables necessary for direct comparison with astronomical data must be calculated along it. Implementing this condition in the proposed set of observational relations profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the average density becomes inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analysed by Ribeiro (1992bRibeiro ( , 1993Ribeiro ( , 1994Ribeiro ( , 1995 for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by , where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a decaying power-law like average density profile, meaning that the dust distribution of this cosmology has a scaling behaviour compatible with the power-law profile of the density-distance correlation observed in the galaxy catalogues.These results show that, in the context of this work, the apparent fractal conjecture is correct.

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Fractals and the Distribution of Galaxies

Cited by 41 publications

References 22 publications

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

Point Distribution as True Quality of LiDAR Point Cloud

Scale Invariance in a Perturbed Einstein-De Sitter Cosmology

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