version (60.6 KB) by Wonsang You
The MATLAB Toolbox for estimating the memory parameter (Hurst exponent), nonfractal connectivity and fractal connectivity


Updated 2 Nov 2018

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It is a MATLAB toolbox for estimating both nonfractal connectivity and fractal connectivity from a set of time series with long-range dependence such as resting state fMRI BOLD signals.

* Getting Started
You can install this toolbox as follows.
1. Place all files of this toolbox at any directory, and add all sub-directories to the MATLAB paths.
2. The wmtsa toolbox should be installed a priori. It can be downloaded from for free.
3. Try to run the demo script "bfn_demo_nonfractal". This demo shows an example of estimating nonfractal connectivity of resting state fMRI BOLD signals of the rat brain using the maximum likelihood estimator.

* Functions
Let X be a NxQ matrix of Q time series with length N. It might be a set of BOLD signals corresponding to multiple ROIs of the brain which was extracted from DICOM images. Then, the function "bfn_mfin_ml" estimates the Hurst exponent, nonfractal connectivity, and fractal connectivity in multivariate time series with long memory using the maximum likelihood method as follows.

[H, nfcon, fcon] = bfn_mfin_ml(X);

H is the Hurst exponent, nfcon and fcon denote the nonfractal connectivity and fractal connectivity respectively. Nonfractal connectivity is identical to the correlation matrix of short memory while fractal connectivity is defined as the asymptotic wavelet correlation of bivariate long memory processes. On the other hand, the function "bfn_mfin_lms" uses the least-mean squares (LMS) method to estimate all the above parameters.

[H, nfcon, fcon] = bfn_mfin_lms(X);

For more options, run the commands "help bfn_mfin_ml" or "help bfn_mfin_lms".

* Reference
Please cite the following paper when using this toolbox.
Wonsang You, Sophie Achard, Joerg Stadler, Bernd Bruekner, and Udo Seiffert, "Fractal analysis of resting state functional connectivity of the brain," in 2012 International Joint Conference on Neural Networks, 2012.

* Information
Please visit the webpage for more information:

You can also view the educational slides:

* Technical supports
Please leave a post to give any question or to report technical issues in the following webpage.

You can also send an e-mail to after subscribing the mailing list.

Cite As

Wonsang You (2022). nonfractal (, GitHub. Retrieved .

You, Wonsang, et al. “Fractal Analysis of Resting State Functional Connectivity of the Brain.” The 2012 International Joint Conference on Neural Networks (IJCNN), IEEE, 2012, doi:10.1109/ijcnn.2012.6252657.

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MATLAB Release Compatibility
Created with R2008b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.