Generating Mandelbrot and Julia sets using PV iterative technique
Year: 2025
Type: article
Abstract: In this study, we utilize the PV iteration method to generate Mandelbrot and Julia sets for the function G ( z ) = z k + 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.
Source: Chaos Solitons & Fractals
Authors: Pragati Gautam, Vineet
Institution: University of Delhi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,970
Funder: University Grants Commission
OpenAlex ID: W4409164675