WHY THE UNIVERSE IS NOT A FRACTAL

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 ∼ 5h-1 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. We present a method based on the minimal spanning tree 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 ±0.1. The correlation dimension differs from this value, D2≃ 1.3±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. © Royal Astronomical Society.