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Generating Mandelbrot and Julia sets using PV iterative technique

Author

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  • 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
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