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A brief note on fractal dynamics of fractional Mandelbrot sets

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  • Wang, Yupin
  • Li, Xiaodi
  • Wang, Da
  • Liu, Shutang

Abstract

This paper preliminary examines a kind of Mandelbrot set generated by a fractional difference quadratic map involving Caputo-like fractional h-difference operators. A connectivity index is proposed based on numerical methods, which avoids difficulties in discussion at the topological level. The dynamics of those sets in two kinds of noise environments are considered involving connectivity, symmetry and dimension. Several typical cases are visualized to illustrate the main conclusions.

Suggested Citation

  • Wang, Yupin & Li, Xiaodi & Wang, Da & Liu, Shutang, 2022. "A brief note on fractal dynamics of fractional Mandelbrot sets," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    • Handle: RePEc:eee:apmaco:v:432:y:2022:i:c:s0096300322004271
    DOI: 10.1016/j.amc.2022.127353
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    3. A. A. Elsadany & A. Aldurayhim & H. N. Agiza & Amr Elsonbaty, 2023. "On the Fractional-Order Complex Cosine Map: Fractal Analysis, Julia Set Control and Synchronization," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    4. Tanveer, Muhammad & Nazeer, Waqas & Gdawiec, Krzysztof, 2023. "On the Mandelbrot set of zp+logct via the Mann and Picard–Mann iterations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 184-204.
    5. Wang, Yupin, 2023. "Fractional quantum Julia set," Applied Mathematics and Computation, Elsevier, vol. 453(C).

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