Efficient Calculation of Fractal Properties via the Higuchi Method

Abstract Higuchi’s method of determining fractal dimension (HFD) is an important research tool that, compared to many other methods, gives rapid, efficient, and accurate estimations for the range of possible fractal dimensions. One major difficulty in applying the method is the correct choice of tuning parameter (kmax) to compute the most accurate results as a poor choice can generate spurious results. We analyze synthetic fractional Brownian motion to offer a general equation that allows determination, a priori, of the best value for the tuning parameter, given a particular length data set.