Fractal Properties of the Cosmic Web

Abstract: The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies joined by filaments and walls, leaving large empty regions called cosmic voids. The most common method of describing the web is a correlation function and its derivative, the fractal function. In this paper, I provide a review of the fractal properties of the cosmic web from the observational point of view within the Newtonian concordance $\Lambda$CDM Universe framework. I give a brief history of fractal studies of the Universe. I then describe the derivation of the fractal function from angular and spatial distributions of galaxies and their relations. Correlation functions are not sensitive to the shape of the galaxy distribution. To improve our quantitative understanding of properties of the web, statistics must be used which are sensitive to the pattern of the web.