Fractal Analysis in MATLAB: A Tutorial for Neuroscientists

Abstract

MATLAB is one of the software platforms most widely used for scien-tifi c computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientifi c data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages and several online tools available for fractal analysis. Keywords Fractal analysis • Fractal dimension • MATLAB 33.1 MATLAB Packages and Toolboxes for Fractal Analysis Boxcount [ 19 ] is one of the fi rst MATLAB scripts developed for computing the fractal dimension (FD) of 1D, 2D, or 3D sets. As its name indicates, Boxcount estimates the FD of a set by using the box-counting method [ 18 ]. It can be only used with binary datasets (for an RGB image, for example, a previous summation of the three components is performed) and the box sizes used to estimate the fractal dimension must be power of two. Boxcount is a MATLAB function that must be integrated into other MATLAB scripts in order to be executed. FracLab [ 14 ] is veteran MATLAB software that allows fractal analysis of 1D signals and 2D images, but analysis of 3D sets is not supported. All the functionality of FracLab is accessible through a graphical interface, so no direct MATLAB programming is needed. FracLab allows the user to calculate not only the fractal dimension of the set but also parameters like the Hölder exponent or multifractal spectra.