An efficient algorithm to determine fractal dimensions of point sets

Based on the Grassberger-Procaccia approach, an efficient, box assisted alg orithm for the determination of the correlation dimension D-2 of a finite p oint set is presented. By invoking a tree like data structure, we are able to handle arbitrary box dimensions d(B) and consequently enhance the effici ency of the calculation compared to methods which only allow for low d(B). The CPU-time consumption of our algorithm is compared to that of the standa rd implementation by applying both methods to the system of three uncoupled Henon maps. A considerable efficiency gain is shown. (C) 2001 Elsevier Sci ence B.V. All rights reserved.