Improved methods for calculating the multifractal spectrum for small data sets

2014 Spring.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