IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v196y2022icp1-14.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000039
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.01.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muhammad Tanveer & Waqas Nazeer & Krzysztof Gdawiec, 2020. "New Escape Criteria for Complex Fractals Generation in Jungck-CR Orbit," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1285-1303, December.
    2. Keten Çopur, Ayşegül & Hacıoğlu, Emirhan & Gürsoy, Faik, 2024. "New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 476-497.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:1-14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.