INCREMENT-BASED ESTIMATORS OF FRACTAL DIMENSION FOR TWO-DIMENSIONAL SURFACE DATA

Abstract

This paper is concerned with estimating the fractal dimension of a surface, given the surface height at locations on a two-dimensional rectangular grid. Some new estimators are proposed and their properties, both numerical and theoretical, are examined. However, before describing the contents of this paper in more detail, we shall briefly review some earlier work on the (simpler) case of one-dimensional sampling.