Fast Multifractal Analysis by Recursive Box Covering

A fractal can be generated by using recursion, and a fractal set of data can be analyzed in the same way. This paper discusses a box-counting algorithm which exploits self-similarity via recursion. The speed of the algorithm is O(n), where n is the number of points in the set. The algorithm is applied to multifractal analysis of the binomial multiplicative process. The algorithm does not involve sorting the floating-point summation; a brief examination of the sorting issue is presented. Scattering for negative q, characteristic of box-counting algorithms, is encountered, and is explained for the simple case of a uniform 1-D set.