(Colorado State University. Libraries, 2014) Anderson, Leif, author; Eykholt, Richard, advisor; Robinson, Raymond Steve, committee member; Gelfand, Martin, committee member; Wu, Mingzhong, committee member; Shipman, Patrick, committee member
There are multiple definitions for fractal dimension, and those definitions disagree. The multifractal spectrum provides a unifying framework for a broad family of definitions of dimension, but it requires large amounts of data to compute. We provide a description of the multifractal spectrum, one existing improvement that improves convergence for small data sets: the Extended Box Algorithm (EBA), and develop several further improvements: Local and Global Norm modifications to the EBA, the a-Norm, the Variable Box size Algorithm (VBA), and the Patchwork method.
