Synopsis of FD3

FD3 is a program that estimates fractal dimension. It was written by John Sarraille and Peter DiFalco, using ideas from "A FAST ALGORITHM TO DETERMINE FRACTAL DIMENSION BY BOX COUNTING", by Liebovitch and Toth, Physics Letters A, 141, 386-390 (1989).

FD3 inputs an ascii list of points, basically one point per line, and outputs box counts at various scales, plus estimates of capacity, information, and correlation dimension.

There are "two-point" estimates of dimension for each scale shift (division of cell size by two), plus overall estimates based on fitting a least-squares line to a log-log plot of cell count versus cell size. FD3 is quite accurate (typically well within 5% when tested on reasonably-sized samples of fractals whose dimension are known exactly) It is quite fast -- O(NlogN) where N is the number of data lines (points) input.

In theory, it will handle any embedding dimension -- points with one coordinate each, two coordinates each, three, four, ... whatever. However, the number of points needed for usable results increases geometrically with the dimension of the set.

More information on how to use FD3 is included within the self-extracting ZIP file (see the files INDEX, README.2, and REPORT.INF).

Copyright (c) 1992 by John Sarraille and Peter DiFalco (

Permission to use, copy, modify, and distribute this software and its documentation for any purpose and without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation.

The algorithm used in this program was inspired by the paper entitled "A Fast Algorithm To Determine Fractal Dimensions By Box Counting", which was written by Liebovitch and Toth, and which appeared in the journal "Physics Letters A", volume 141, pp 386-390, (1989).

This program is not warranteed: use at your own risk.