IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v196y2025ics0960077925003595.html
   My bibliography  Save this article

Generating Mandelbrot and Julia sets using PV iterative technique

Author

Listed:
  • Gautam, Pragati
  • Vineet,

Abstract

In this study, we utilize the PV iteration method to generate Mandelbrot and Julia sets for the function G(z)=zk+c. We establish escape criterion conditions for the PV iteration and provide a variety of graphical examples for different parameter settings. We also compare the graphs with those generated by other well-known iterations, such as the Picard-Mann and M iterations. Furthermore, we investigate the dependency between the iteration’s parameters and three numerical measures: the average escape time (AET), the non-escaping area index (NAI), and the fractal generation time. A comparative analysis is conducted with the renowned Mann, Picard-Mann, and M iteration methods. The results demonstrate that the fractals generated by the PV iteration exhibit distinct characteristics compared to those generated by other iterations, with non-linear dependencies that vary between different methods. These findings highlight the unique properties and potential applications of PV iteration in fractal generation.

Suggested Citation

  • Gautam, Pragati & Vineet,, 2025. "Generating Mandelbrot and Julia sets using PV iterative technique," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003595
    DOI: 10.1016/j.chaos.2025.116346
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925003595
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116346?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. Qura Tul Ain & Ji-Huan He & Xiao-Li Qiang & Zheng Kou, 2024. "The Two-Scale Fractal Dimension: A Unifying Perspective To Metabolic Law," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-11.
    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.
    4. Rawat, Shivam & Prajapati, Darshana J. & Tomar, Anita & Gdawiec, Krzysztof, 2024. "Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with s-convexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 148-169.
    5. Nawaz, Bashir & Ullah, Kifayat & Gdawiec, Krzysztof, 2024. "Generation of Mandelbrot and Julia sets by using M-iteration process," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    6. Francisco Martinez & Hermann Manriquez & Alberto Ojeda & Gabriel Olea, 2022. "Organization Patterns of Complex River Networks in Chile: A Fractal Morphology," Mathematics, MDPI, vol. 10(11), pages 1-23, May.
    Full references (including those not matched with items on IDEAS)

    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. 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. Nawaz, Bashir & Ullah, Kifayat & Gdawiec, Krzysztof, 2024. "Generation of Mandelbrot and Julia sets by using M-iteration process," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    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.
    4. Mohammad (Behdad) Jamshidi & Arash Dehghaniyan Serej & Alireza Jamshidi & Omid Moztarzadeh, 2023. "The Meta-Metaverse: Ideation and Future Directions," Future Internet, MDPI, vol. 15(8), pages 1-31, July.
    5. Adhikari, Nabaraj & Sintunavarat, Wutiphol, 2024. "The Julia and Mandelbrot sets for the function zp−qz2+rz+sincw exhibit Mann and Picard–Mann orbits along with s-convexity," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. 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).
    7. Rawat, Shivam & Prajapati, Darshana J. & Tomar, Anita & Gdawiec, Krzysztof, 2024. "Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with s-convexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 148-169.
    8. Sharma, Saurabh & Tomar, Anita & Padaliya, Sanjay Kumar, 2025. "On the evolution and importance of the Fibonacci sequence in visualization of fractals," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    9. Francisco Martínez & Bastian Sepúlveda & Hermann Manríquez, 2023. "Fractal Organization of Chilean Cities: Observations from a Developing Country," Land, MDPI, vol. 12(2), pages 1-21, January.

    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:chsofr:v:196:y:2025:i:c:s0960077925003595. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.