Yongfeng Wu

Date of Award


Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)




David J.Batuski

Second Committee Member

André Khalil

Third Committee Member

James McClymer


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, box counting, and the ¡ 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 a sample’s output functions, which characterize the distributions in multi-parameter space. We also developed both the Box Counting method and Perimeter-Area Dimension method with the Hexagon Cell technique to calculate the fractal dimension of our samples. We use a dozen slices of a volume of space containing many newly measured galaxies from Sloan Digital Sky Survey Data Release 5. We compare results with that of mock samples of galaxies from N-body simulation with current best estimates of cosmological parameters and nestedpairs simulations, and random catalogs. By systematically studying those slices including hundreds of thousands of galaxies, we demonstrated that in the local universe there exists a fractal structure from MST. We also discuss the possible improvement for mock samples.