Academic Journal
On the Application of Mann-Iterative Scheme with h-Convexity in the Generation of Fractals
| العنوان: | On the Application of Mann-Iterative Scheme with h-Convexity in the Generation of Fractals |
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| المؤلفون: | Asifa Tassaddiq, Muhammad Tanveer, Muhammad Zubair, Muhammad Arshad, Carlo Cattani |
| المصدر: | Fractal and Fractional, Vol 8, Iss 7, p 414 (2024) |
| بيانات النشر: | MDPI AG, 2024. |
| سنة النشر: | 2024 |
| المجموعة: | LCC:Thermodynamics LCC:Mathematics LCC:Analysis |
| مصطلحات موضوعية: | Mann iteration with h-convexity (MIH), escape criterion, complex polynomial function, Mandelbrot set (M-set), Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433 |
| الوصف: | Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation from this fact, we generate and analyze fractals as an application of the proposed Mann iterative technique with h-convexity. By doing so, we develop an escape criterion for it. Using this established criterion, we set the algorithm for fractal generation. We use the complex function f(x)=xn+ct, with n≥2,c∈C and t∈R to generate and compare fractals using both the Mann iteration and Mann iteration with h-convexity. We generalize the Mann iterative scheme using the convexity parameter h(α)=α2 and provide the detailed representations of quadratic and cubic fractals. Our comparative analysis consistently proved that the Mann iteration with h-convexity significantly outperforms the standard Mann iteration scheme regarding speed and efficiency. It is noticeable that the average number of iterations required to perform the task using Mann iteration with h-convexity is significantly less than the classical Mann iteration scheme. Moreover, the relationship between the fractal patterns and the input parameters of the proposed iteration is extremely intricate. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 2504-3110 |
| Relation: | https://www.mdpi.com/2504-3110/8/7/414; https://doaj.org/toc/2504-3110 |
| DOI: | 10.3390/fractalfract8070414 |
| URL الوصول: | https://doaj.org/article/61809981a1c740e8a7fd84ee539cf257 |
| رقم الانضمام: | edsdoj.61809981a1c740e8a7fd84ee539cf257 |
| قاعدة البيانات: | Directory of Open Access Journals |
| تدمد: | 25043110 |
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| DOI: | 10.3390/fractalfract8070414 |