ON THE PRACTICE OF ESTIMATING FRACTAL DIMENSION

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating "fractal dimension," the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectral and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.