Fractal dimension of basin boundaries calculated using the basin entropy

André Gusso and Leandro E. de Mello

Chaos, Solitons & Fractals, 2021, vol. 153, issue P2

Abstract: The concept of basin entropy (Sb) was recently introduced as a means to characterize basins of attraction with regard to their complexity. It was also found a connection between Sb and the uncertainty exponent α. This connection allows the calculation of the fractal dimension d of the basin boundary between two basins of attraction. However, this method of calculation has not been explored in the literature. In this work we evaluate the performance of the method based upon the basin entropy in the calculation of the fractal dimension of basin boundaries. For that purpose, the method is applied to the calculation of d for several artificial uniform fractals, such as the Koch island and the Sierpinski Carpet, and the values obtained are compared with the exact dimensions obtained by analytical methods. It is concluded that excellent results are generally obtained if the boxes used in the calculation of Sb are chosen adequately, and a simple criterion for this choice is proposed. Numerical arguments are provided to justify the exclusion of small boxes with low resolution in the calculation of d. While the investigation is motivated by the calculation of d for basin boundaries, the method can be applied to any image containing two distinct regions with a boundary, whose dimension has to be determined.

Keywords: Fractal dimension; Uncertainty exponent; Basin entropy; Basins of attraction (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008869

DOI: 10.1016/j.chaos.2021.111532

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