Distribution of Galaxies: Scaling vs. Fractality

Abstract

The distribution of matter in the Universe is probably the oldest paradigm of fractality. In the major part of the literature devoted to this theme, which is already ancient, models of fractal structures are first constructed, then checked against observations. This short course will present a converse approach. The data about the actual distribution of galaxies in the 10 to 100 Mpc range are now rather precise and reliable, and we can thus start from them so as to derive the fractal properties of the set. We shall give below in a self-contained way the main ideas of this construction; the figures, equations, detailed derivations, discussions and references can be found in two articles [1,2] denoted here as I and II. We shall focus less on astrophysical implications than on general methods which may be of interest for other problems.