A revisitation of the triangular prism surface area method for estimating the fractal dimension of fractal surfaces

Abstract

Fractal dimension is widely used to give a measure of variability and roughness of curves, signals, objects, sta- tistical distributions, and so on, We found that an often used method, the so-called triangular prism surface- area method, for estimating the tractal dimension of fractal surfaces possesses some intrinsic mistake., in appli- cation. This note describes the misintel"pretation and suggests the proper application, that we calI Revised Tri- angular Prism Method (RTPM). To show its feasibility we apply RTPM to some synthetic Euclidean and frac- tal surfaces of known dimension.

Keywords

• Fractal dimension
• self-affinity
• self-similarity
• triangulation