Determination of f(alpha) for a limited random point set

Details Determination of f(alpha) for a limited random point set Determination of f(alpha) for a limited random point set

Oct 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrva..40.3954a&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 40, Oct. 1, 1989, p. 3954-3963.

Mathematics

Dynamical Systems

20

Fractals, Random Processes, Spatial Distribution, Spectral Methods, Astronomical Catalogs, Chaos, Dynamical Systems, Mass Distribution

Scientific paper

The use of f(alpha) spectra to characterize multifractals has gained increasing attraction during recent years. There are basically two procedures to determine f(alpha) from a given point distribution, both offering a number of approaches with different details in the methods. Three of these approaches are applied to the specific example of the galaxy distribution as compiled in the Zwicky et al. Catalog of Galaxies and Clusters of Galaxies (1962-1968). As points of particular importance with respect to the finiteness of the sample, the influence of boundary effects, the behavior of rms erros in alpha and f(alpha), and differing notions of locality in the different approaches are presented and discussed.

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