Srivastava, Rekha and Tassaddiq, Asifa and Kasmani, Ruhaila Md. (2024) Escape Criteria Using Hybrid Picard S-Iteration Leading to a Comparative Analysis of Fractal Mandelbrot Sets Generated with S-Iteration. Fractal and Fractional, 8 (2). p. 116. ISSN 2504-3110, DOI https://doi.org/10.3390/fractalfract8020116.
Full text not available from this repository.Abstract
Fractals are a common characteristic of many artificial and natural networks having topological patterns of a self-similar nature. For example, the Mandelbrot set has been investigated and extended in several ways since it was first introduced, whereas some authors characterized it using various complex functions or polynomials, others generalized it using iterations from fixed-point theory. In this paper, we generate Mandelbrot sets using the hybrid Picard S-iterations. Therefore, an escape criterion involving complex functions is proved and used to provide numerical and graphical examples. We produce a wide range of intriguing fractal patterns with the suggested method, and we compare our findings with the classical S-iteration. It became evident that the newly proposed iteration method produces novel images that are more spontaneous and fascinating than those produced by the S-iteration. Therefore, the generated sets behave differently based on the parameters involved in different iteration schemes.
| Item Type: | Article |
|---|---|
| Funders: | Deanship of Postgraduate Studies and Scientific Research at Majmaah University |
| Uncontrolled Keywords: | picard iteration; S-iteration; Mandelbrot sets; hybrid Picard S-iteration |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 11 Nov 2024 00:55 |
| Last Modified: | 11 Nov 2024 00:55 |
| URI: | http://eprints.um.edu.my/id/eprint/45704 |
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