On the Construction of a Fractal Spectrum for Data Analysis

Abstract

Multifractal probability distributions are defined as mixture of n monofractal distributions. The exponents i are the fractal dimensions which determine the information- filling property of an observation i from this distribution. A useful device for examining multifractal observations is the multifractal spectrum. The fractal spectrum was shown to be a one–to–one function, monotonically increasing with x on a logarithmic scale for non–fractal distributions. Similarly, multifractal distributions viewed on a larger scale (s) have a spectrum that behaves like power function As-k but when viewed on a smaller scale, it behaves like a concave downward quadratic function A(s - so)2 + B(s - so) + C where A, B and C are parameters to be estimated.