Determination of Fractal Dimensions of Single-Valued Surfaces in 3-Space in the Presence of Uniformly and Normally Distributed Random Noise: The Triangulation Algorithm.

This report describes a new and efficient algorithm for determining the Mandelbrot fractal dimension of single-value surfaces in 3-space. First the algorithm is shown to return appropriate values for the fractal dimensions of Brown constructions. Then, in order to elucidate the errors introduced into measured fractal dimensions by experimental uncertainties, the algorithm is applied to Brown surfaces that have been distorted by the addition of uniformly and normally distributed noise. Since the results apply to single-valued subsections of multiple-valued surfaces, they are also representative of the effects of uniformly and normally distributed noise on the apparent fractal scaling of multiple-valued surfaces.