Escape criteria using hybrid Picard S-iteration leading to a comparative analysis of fractal Mandelbrot sets generated with S-iteration

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dc.contributor.authorSrivastava, Rekha
dc.contributor.authorTassaddiq, Asifa
dc.contributor.authorKasmani, Ruhaila Md
dc.date.accessioned2024-10-10T17:23:12Z
dc.date.available2024-10-10T17:23:12Z
dc.date.issued2024
dc.description.abstractFractals 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.
dc.description.reviewstatusReviewed
dc.description.scholarlevelFaculty
dc.description.sponsorshipThe author extends the appreciation to the Deanship of Postgraduate Studies and Scientific Research at Majmaah University for funding this research work through the project number (ICR-2024-949).
dc.identifier.citationSrivastava, R., Tassaddiq, A., & Kasmani, R. M. (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), Article 2. https://doi.org/10.3390/fractalfract8020116
dc.identifier.urihttps://doi.org/10.3390/fractalfract8020116
dc.identifier.urihttps://hdl.handle.net/1828/20560
dc.language.isoen
dc.publisherFractal and Fractional
dc.rightsAttribution CC BY
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleEscape criteria using hybrid Picard S-iteration leading to a comparative analysis of fractal Mandelbrot sets generated with S-iteration
dc.typeArticle

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