How do you find the fractal dimension in Matlab?
The result is a fractal set (or “fractal dust”) of dimension DF = D + log(P)/log(2) < D. The following example generates a 2048×2048 image with probability P=0.8, i.e. fractal dimension DF = 1.678.
What is the equation for fractal dimension?
Fractal Dimensions of Geometric Objects. In the last section, we learned how scaling and magnification relate to dimension, and we saw that the dimension, D, can be seen as the log of the number of pieces divided by the log of the magnification factor. Expressed as an equation, we have D = log(N) / log(r).
What is Box counting method?
Box counting is a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc. into smaller and smaller pieces, typically “box”-shaped, and analyzing the pieces at each smaller scale.
What is FracLac?
FracLac is a plugin for ImageJ. It is freely available software developed and maintained by our lab at the School of Community Health, Faculty of Science, Charles Sturt University, Australia. The author of the software and project lead is also the author of this document (me, Audrey Karperien).
Are there half dimensions?
It turns out, however, that for some sets that are not well-behaved (naughty ones?), the Hausdorff dimension can be fractional. The Koch snowflake, for example, has a Hausdorff dimension which is greater than 1 and smaller than 2, suggesting that it is somehow more substantial than a line, but less than a plane.
How to calculate a fractal dimension in MATLAB?
For example, the function ‘randcantor’ provided with the package generates a 1D, 2D or 3D generalized random Cantor set. This set is obtained by iteratively dividing an initial set filled with 1 into 2^D subsets, and setting each subset to 0 with probability P.
How is the fractal dimension ( fd ) image generated?
The fractal dimension (FD) image is generated by considering each pixel in the original CT image as a single fractal dimension estimated from its 7×7 neighbours. The FD generated image remarkably enhances the tissue texture, and the internal subtle structures become more obvious as compared to the original CT image.
Who is the copyright holder of fractal dimension?
Copyright (c) 2009, Omar Al-Kadi All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
How to calculate the fractal dimension of EEG?
Then, depending on the chosen method (Katz, Higuchi, Fractional Brownian Motion), the fractal dimension for each channel will be calculated in each frequncy band for each subject. Next, the results from a t-test, comparing the results from the two groups, is used for the topoplots.
