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 multi­ple 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 ga­laxies from N-body simulation nested-pairs simulations and random catalogs. By systematically studying hundreds of thousands of ga­laxies we demonstrate that in the local universe there exists a fractal structure from MST. We also discuss the possible improvement for mock samples.