Measuring the Fractal Dimension of Natural Surfaces Using a Robust Fractal Estimator

Abstract

In this paper, we introduce a new technique for computing the fractal dimension, D, of the topography of natural surfaces. The method is designed to overcome some of the limitations evident in some existing methods. Discussion focuses on the critical relationship between analytical cartography and empirical cartometry, the taking of measurements from maps. The new method, the robust fractal estimator, produces results that are inconsistent with some other methods, and the discussion concentrates on the relative merits of empirical versus analytical reasoning in isolating the cause of the discrepancy.