NEW FRACTAL SETS COINED FROM FRACTIONAL MAPS

Yupin Wang (), Shutang Liu and Hui Li ()
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Yupin Wang: School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, P. R. China
Shutang Liu: School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China
Hui Li: School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-12

Abstract: This paper proposes a criterion for fractionalizing traditional fractal sets, and reports several fractional generalizations of the Julia set and Mandelbrot set of the classic quadratic map. The discrepancies among those extensions are investigated preliminarily. The influence of the map’s memory effect on its fractal sets is discussed through visualization techniques and dimension analysis.

Keywords: Fractional Calculus; Quadratic Map; Julia Set; Mandelbrot Set; Fractal (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0218348X21502704

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