Box-counting multifractal analysis

Abstract

Two box-counting algorithms for the determination of generalized fractal dimensions are described. Results of application of the algorithms to Euclidean curves, quadric islands, Koch symmetric and asymmetric triadic snowflakes, and split snowflake halls introduced by Mandelbrot [Fractal Geometry of Nature (Freeman, New York, 1983)] are described. Comparison to analytic results for the model curves is provided and the effectiveness of the algorithms is discussed.