Why the universe is not a fractal

Details Why the universe is not a fractal Why the universe is not a fractal

Feb 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.242..517m&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 242, Feb. 1, 1990, p. 517-521.

Astronomy and Astrophysics

Astronomy

63

Cosmology, Galactic Evolution, Universe, Astronomical Spectroscopy, Red Shift, Spatial Distribution

Scientific paper

There is overwhelming evidence from the CfA redshift survey that the distribution of galaxies in the Universe obeys a scaling law on length scales less than 5/h Mpc. Despite this scale invariance, the Universe is not well represented by a homogeneous fractal on these scales. The dependence of the correlation length r0 with sample depth and luminosity is studied. A method based on the minimal spanning tree is presented for determining the Hausdorff dimension, DH, of a point distribution. The technique is applied in order to find the Hausdorff dimension of the CfA redshift survey. The obtained value is DH = 2.1 + or - 0.1. The correlation dimension differs from this value, D2 = 1.3 + or - 0.1, therefore the Universe is not well characterized by only one exponent: it is not a simple fractal. It is a more complex structure, a multifractal.

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