There is no built-in function in MATLAB for finding fractal dimensions. However, a third-party product, FRACLAB, is available at the following address:
For the special case of a family of stochastic precesses named fractional Brownian motion. The WFBMESTI function performs the fractal dimension estimation (evaluation) of the associated parameter.
Let us explain the connection with fractal dimension. A fractional Brownian motion (fBm) is a continuous-time Gaussian process depending on the Hurst parameter 0 < H < 1. It generalizes the ordinary Brownian motion corresponding to H = 0.5 and whose derivative is the white noise. The fBm is self-similar in distribution and the variance of the increments is given by
Var(fBm(t)-fBm(s)) = v t-s^(2H)
where v is a positive constant. The local regularity of the sample paths is related to the fractal dimension which directly controlled by the parameter H.
WFBMESTI performs the parameter estimation of fractional Brownian motion starting from a realization.
WFBMESTI provides three different estimates and the second one is based on wavelets. More precisely, the first one, due to Istas and Lang, is based on the discrete second-order derivative. The second one is a wavelet-based adaptation and has similar properties. The third one, proposed by Flandrin, estimates H using the slope of the loglog plot of the detail variance versus the level.
