On the multifractal analysis of galaxy catalogs with box-counting methods

Details On the multifractal analysis of galaxy catalogs with box-counting methods On the multifractal analysis of galaxy catalogs with box-counting methods

Sep 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...289..667d&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 289, no. 3, p. 667-672

Mathematics

Probability

10

Astronomical Catalogs, Cosmology, Fractals, Galaxies, Mass Distribution, Statistical Analysis, Distribution Moments, Poisson Equation, Probability Theory, Set Theory

Scientific paper

The influence of sampling and discreteness effects on multifractal (MFR) analysis performed with box-counting methods is discussed. Emphasis is put on the uniform mass (counting) measure, which is used in most analysis in astronomy. Finite sampling is shown to lead to a spurious point (alpha = 0, f(alpha) = 0) in the MFR spectrum. Such effect can give to a real fractal the appearance of a fractal with two scaling regimes. To avoid such effect, one might be tempted to perform analysis at scales larger than the mean interparticle distance. This is shown to give meaningless results and leads to the loss of the connection between Renyi dimensions and MFR spectrum. All these effects are illustrated on simple examples.

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