The Use of Generalized Information Dimension in Measuring Fractal Dimension of Time Series

Abstract

An algorithm for calculating generalized fractal dimension of a time series using the general information function is presented. The algorithm is based on a strings sort technique and requires $O(N \log_2 N)$ computations. A rough estimate for the number of points needed for the fractal dimension calculation is given. The algorithm was tested on analytic example as well as well-known examples, such as, the Lorenz attractor, the Rossler attractor, the van der Pol oscillator, and the Mackey-Glass equation, and compared, successfully, with previous results published in the literature. The computation time for the algorithm suggested in this paper is much less then the computation time according to other methods.Comment: 12 latex pages (including 15 figures; fig1-fig7d). Computer programs can be found at http://faculty.biu.ac.il/~ashkenaz/FDprog/ To be published in Physica