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Fractal Analysis Programs of the National Simulation Resource


Our long range purpose is to provide a set of analytical tools for fractal analysis. We currently have programs available for the generation of synthetic 1-dimensional signals that are simple fractional Brownian noise, and analysis programs for determining the fractal dimension D (or the Hurst coefficient H, H = E + 1 - D, where E is the Euclidean dimension) from a simple fractal time series, i.e. a 1-dimensional signal. The analysis methods are described briefly by Schepers, van Beek, and Bassingthwaighte (1992) and in more detail by Bassingthwaighte, Liebovitch, and West (1994), which also reviews applications. Specific publications on the methods are listed with the programs.

A short description of the programs currently available for distribution is given below. Each package includes the source code for the product, its test program, and all subprograms upon which they depend. Also included are a README file with notes about the files, a manual page (plain text and UNIX troff source versions), a Makefile to create and run the test program, and the auxiliary files required by the test program.

These software packages can be transferred using anonymous ftp by clicking on the name of the package desired. Transferred files are compressed tar archives. (Some browsers will uncompress the file automatically). Extracting files from the archive will place the source files in a new subdirectory with the same name as the program.

(NOTE: Beyond NSR, Francesco Potortì has made available, under the Gnu Public License, some small Octave functions for measuring and generating the Hurst parameters of unidimensional fractional Brownian noise. These functions can be obtained via his Software Page.)

Available Programs (All programs in FORTRAN except flowrect which is written in C)

(Updated to compile and run on Linux OS unless noted, original code ran on Sun OS)

Signal generating programs

Signal analysis programs

Analysis Programs. See Cannon et al. (1997) for details for swv, bdswv and ldswv.

Problems and Questions

To report any problems or obtain further information, send e-mail to: Gary Raymond


Bassingthwaighte JB and Raymond GM. Evaluating rescaled range analysis for time series. Ann. Biomed. Eng. 22:432-444, 1994.

Bassingthwaighte JB and Raymond GM. Evaluation of the dispersional analysis method for fractal time series. Ann. Biomed. Eng. 23:491-505, 1995.

Bassingthwaighte JB, Liebovitch LS and West BJ. Fractal Physiology. New York, London: Oxford University Press, 1994.

Caccia DC, Percival DB, Cannon MJ, Raymond G and Bassingthwaighte JB. Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods. Physica A 246: 609-632, 1997.

Cannon MJ, Percival DB, Caccia DC, Raymond GM and Bassingthwaighte JB. Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series. Physica A 241: 606-626, 1997.

Davies RB, Harte DS. Tests for Hurst Effecti. Biometrika, (1987) 74, 95-101.

Kendziorski CM, Bassingthwaighte JB and Tonellato PJ. Evaluating maximum likelihood estimation methods to determine the Hurst coefficient. Physica A 273: 439-451, 1999.

Peitgen HO and Saupe D. The Science of Fractal Images. Tokyo, Springer, Springer: Springer Verlag, 1988.

Percival DB, Simulating Gaussian Random Processes with Specified Spectra. Computing Science and Statics, 24 (1992) pp. 534-538..

Raymond GM and Bassingthwaighte JB. Deriving dispersional and scaled windowed variance analyses using the correlation function of discrete fractional Gaussian noise. Physica A 265: 85-96, 1999.

Raymond GM, Percival DB and Bassingthwaighte JB. The spectra and periodograms of anti-correlated discrete fractional Gaussian noise. Physica A 2003 May 1: 322:169-179.

Schepers, H. E., J. H. G. M. van Beek, and J. B. Bassingthwaighte. Comparison of four methods to estimate the fractal dimension from self-affine signals. IEEE Eng. Med. Biol. 11:57-64x71, 1992.

Last modified 16Apr13, 12:31 pm.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.