College of Science and Health Theses and Dissertations

Date of Award

Summer 8-19-2018

Degree Type


Degree Name

Master of Science (MS)



First Advisor

Jesus Pando, PhD


The study of large scale structure (LSS) of the Universe armed with both all-sky surveys and numerical simulations has become an increasingly important tool to probe basic cosmology. We used the method of wavelet transforms combined with the fractal based point-processes to investigate the clustering of matter on galactic scales through the fractal analysis approach. In particular, we developed a method to calculate the angular fractal dimension of galaxy distributions as a function of the cosmological comoving space. Taking advantage of the self-similarity and lo- calization properties of the wavelets, allows us to compute the fractal dimension of galaxies in narrow redshift bins. The narrow bins assure that dynamical evolution has not occurred. We used both real and simulated data from the Baryon Oscilla- tion Spectroscopic Survey (BOSS) and the Mock Galaxy Catalogs produced by the Sloan Digital Sky Survey (SDSS). Using the wavelet packet power spectrum, we find areas in the galaxy distribution which have power law like behavior. The exponent of the power law is the Hurst exponent H, which is directly related to the fractal dimension of spatial point processes. We find the fractal dimension at all redshifts is D = 1:3+0:2 for BOSS Galaxies while D = 1:6+0:3 for Mock Galaxy Catalogs. We concluded that galaxies distribution in the redshift range z < 1 can be described as angular fractal systems, and the distribution is inhomogenous and irregular.

SLP Collection


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Physics Commons