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Exploring the Julia and Mandelbrot sets of zp+logct using a four-step iteration scheme extended with s-convexity

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  • Adhikari, Nabaraj
  • Sintunavarat, Wutiphol

Abstract

Iterative approaches have been established to be fundamental for the creation of fractals. This paper introduces an approach to visualize Julia and Mandelbrot sets for a complex function of the form Q(z)=zp+logct for all z∈ℂ, where p∈N∖{1},t∈[1,∞),c∈ℂ∖{0}, using a four-step iteration scheme extended with s-convexity. The study introduces an escape criteria for generating Julia and Mandelbrot sets using a four-step iterative method. It investigates how changes in the iteration parameters influence the shape and color of the resulting Julia and Mandelbrot sets. This approach can generate a wide range of captivating fractals and analyze them through numerical experiments.

Suggested Citation

  • Adhikari, Nabaraj & Sintunavarat, Wutiphol, 2024. "Exploring the Julia and Mandelbrot sets of zp+logct using a four-step iteration scheme extended with s-convexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 357-381.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:357-381
    DOI: 10.1016/j.matcom.2024.01.010
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    References listed on IDEAS

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    1. S. L. Singh & Charu Bhatnagar & S. N. Mishra, 2005. "Stability of Jungck-type iterative procedures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-9, January.
    2. Kumari, Sudesh & Gdawiec, Krzysztof & Nandal, Ashish & Postolache, Mihai & Chugh, Renu, 2022. "A novel approach to generate Mandelbrot sets, Julia sets and biomorphs via viscosity approximation method," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Tassaddiq, Asifa, 2022. "General escape criteria for the generation of fractals in extended Jungck–Noor orbit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 1-14.
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