Some Remarks on the Numerical Estimation of Fractal Dimension

Abstract

Fractal geometry is currently of major interest in many fields. A commonly occurring problem involves determining the fractal dimension. Hausdorff (1919) rigorously defined the concept of fractional dimension, and further theoretical work was done by Besicovitch and others (see Falconer, 1985 or 1990, for an extensive list of references). Few applications were made using the concept of fractals until the early 1970s when Mandelbrot began his work. In the past ten years, many researchers (e.g., Grassberger, 1983; Barton and Larson, 1985; Sreenivasan and Meneveau, 1986; and Hunt and Sullivan, 1989) from a wide variety of disciplines have devised algorithms for estimating fractal dimensions.