On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals.
Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. We also demonstrate the imp...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0312197 |
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| author | Khairul Habib Alam Yumnam Rohen Naeem Saleem Maggie Aphane Asima Razzaque |
| author_facet | Khairul Habib Alam Yumnam Rohen Naeem Saleem Maggie Aphane Asima Razzaque |
| author_sort | Khairul Habib Alam |
| collection | DOAJ |
| description | Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with numerical examples and graphical illustrations using the MATHEMATICA software, algorithm, and colormap. Moreover, we observe that the Julia set appears when we widen the Mandelbrot set at its petal edges, suggesting that each Mandelbrot set point contains a sizable quantity of Julia set picture data. It is commonly known that fractal geometry may capture the complexity of many intricate structures that exist in our surroundings. |
| format | Article |
| id | doaj-art-b2694d35ed6f46c698198b177c71ee1f |
| institution | Kabale University |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-b2694d35ed6f46c698198b177c71ee1f2025-01-17T05:31:38ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01201e031219710.1371/journal.pone.0312197On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals.Khairul Habib AlamYumnam RohenNaeem SaleemMaggie AphaneAsima RazzaqueOur study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with numerical examples and graphical illustrations using the MATHEMATICA software, algorithm, and colormap. Moreover, we observe that the Julia set appears when we widen the Mandelbrot set at its petal edges, suggesting that each Mandelbrot set point contains a sizable quantity of Julia set picture data. It is commonly known that fractal geometry may capture the complexity of many intricate structures that exist in our surroundings.https://doi.org/10.1371/journal.pone.0312197 |
| spellingShingle | Khairul Habib Alam Yumnam Rohen Naeem Saleem Maggie Aphane Asima Razzaque On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. PLoS ONE |
| title | On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. |
| title_full | On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. |
| title_fullStr | On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. |
| title_full_unstemmed | On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. |
| title_short | On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. |
| title_sort | on escape criterion of an orbit with s convexity and illustrations of the behavior shifts in mandelbrot and julia set fractals |
| url | https://doi.org/10.1371/journal.pone.0312197 |
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