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General escape criteria for the generation of fractals in extended Jungck–Noor orbit

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  • Tassaddiq, Asifa

Abstract

The aesthetic patterns play a key role in the field of fractals. Due to self similarities in the nature of fractals, researchers used the fractals in many fields of sciences (i.e. in Mathematics, Computer Science, Physics, Image Encryption, Biology and Chemistry). The most studied fractals types are the Mandelbrot sets (MSs) and Julia sets (JSs). To generate fractals, escape criteria is required. In this work, a general escape criteria is proved via extended Jungck-Noor iteration with s-convexity. These results are used in algorithms to present the generation of fractals in extended Jungck-Noor orbit for general complex polynomial f(x)=∑i=0paixi with p≥2, where ai∈ℂ for i=0,1,2,…,p. The graphics of MSs and JSs are demonstrated in the examples. The variations in MSs and JSs for different values of involved parameters are also shown.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:1-14
    DOI: 10.1016/j.matcom.2022.01.003
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    References listed on IDEAS

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    1. Nawab Hussain & Vivek Kumar & Marwan A. Kutbi, 2013. "On Rate of Convergence of Jungck-Type Iterative Schemes," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, May.
    2. Yuanyuan Sun & Lina Chen & Rudan Xu & Ruiqing Kong, 2014. "An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-9, January.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.

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