DIMENSIONALITY ANALYSIS OF PATTERNS - FRACTAL MEASUREMENTS

Since the advent of Mandelbrot's fractal geometry in 1975, many geolog ical and geophysical patterns have been characterized by their fractal scaling properties. The purpose of this paper is to present and compa re standard and new methods used to estimate the fractal dimension of random (natural) fractals. Examples demonstrate the relative limitatio ns of the techniques, and the modifications necessary to more accurate ly estimate the scaling properties of certain types of fractals. Discu ssion and examples include branching diffusion-limited aggregates, fra cture surfaces, and fractional Brownian surfaces.