The Fractal Structure of the Universe

The fractal dimension of the spatial distribution of galaxies can be characterized by various statistical and topological methods, such as the Two-point Correlation Function, Perimeter-Area, Box Counting, and the Gamma Function. Here we develop a new way to get fractal information, that is the Metric Space Technique (MST). It allows multi-ple measures to be simultaneously applied for quantitative analysis of any type of structure distribution. All such distributions are considered to be elements of multi-parameter space, and the analysis is based on considering output functions, which characterize the distributions in multi-parameter space. We also develop both the Box Counting and Perimeter-Area method with the Hexagon Cell technique to calculate the fractal dimension of our samples. We compare results from Sloan Digital Sky Survey Data Release 5 with that of mock samples of ga-laxies from N-body simulation, nested-pairs simulations and random catalogs. By systematically studying hundreds of thousands of ga-laxies, we demonstrate that in the local universe there exists a fractal structure from MST. We also discuss the possible improvement for mock samples.