Journal
CHAOS SOLITONS & FRACTALS
Volume 113, Issue -, Pages 46-52Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2018.05.001
Keywords
Pickover biomorphs; Self-similar structures; Fractals; Hyperbolic complex numbers; Moran autocorrelation function; Sample entropy; Hurst exponent
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Funding
- University of Wroclaw [0401/0449/17]
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In this study Pickover biomorphs are analysed as being dependent on the chosen complex number system in which iterations of analytic functions are performed. Moran's spatial autocorrelation function and two forms of entropy, the Shannon entropy and the sample entropy, are chosen in order to find correlations and measure complexity in Pickover biomorphs. These turn out to be strongly correlated and low-entropy objects with a fractal dimension between 1.4 and 2. It is shown that there is a strong maximum in correlation and a strong minimum in entropy for the case of Galilean complex numbers corresponding to the square of the generalised imaginary unit being equal to zero. (C) 2018 Elsevier Ltd. All rights reserved.
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