Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method
This article investigates and analyzes the diverse patterns of Julia sets generated by new classes of generalized exponential and sine rational functions. Using a generalized viscosity approximation-type iterative method, we derive escape criteria to visualize the Julia sets of these functions. This...
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MDPI AG
2025-04-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/4/322 |
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| author | Iqbal Ahmad Ahmad Almutlg |
| author_facet | Iqbal Ahmad Ahmad Almutlg |
| author_sort | Iqbal Ahmad |
| collection | DOAJ |
| description | This article investigates and analyzes the diverse patterns of Julia sets generated by new classes of generalized exponential and sine rational functions. Using a generalized viscosity approximation-type iterative method, we derive escape criteria to visualize the Julia sets of these functions. This approach enhances existing algorithms, enabling the visualization of intricate fractal patterns as Julia sets. We graphically illustrate the variations in size and shape of the images as the iteration parameters change. The new fractals obtained are visually appealing and attractive. Moreover, we observe fascinating behavior in Julia sets when certain input parameters are fixed, while the values of <i>n</i> and <i>m</i> vary. We believe the conclusions of this study will inspire and motivate researchers and enthusiasts with a strong interest in fractal geometry. |
| format | Article |
| id | doaj-art-383c6e01cf4f4b78b8b90c105dc6a4cd |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-383c6e01cf4f4b78b8b90c105dc6a4cd2025-08-20T02:17:20ZengMDPI AGAxioms2075-16802025-04-0114432210.3390/axioms14040322Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative MethodIqbal Ahmad0Ahmad Almutlg1Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Saudi ArabiaThis article investigates and analyzes the diverse patterns of Julia sets generated by new classes of generalized exponential and sine rational functions. Using a generalized viscosity approximation-type iterative method, we derive escape criteria to visualize the Julia sets of these functions. This approach enhances existing algorithms, enabling the visualization of intricate fractal patterns as Julia sets. We graphically illustrate the variations in size and shape of the images as the iteration parameters change. The new fractals obtained are visually appealing and attractive. Moreover, we observe fascinating behavior in Julia sets when certain input parameters are fixed, while the values of <i>n</i> and <i>m</i> vary. We believe the conclusions of this study will inspire and motivate researchers and enthusiasts with a strong interest in fractal geometry.https://www.mdpi.com/2075-1680/14/4/322algorithmsescape criteriaJulia setsiterative methodsgeneralized rational functions |
| spellingShingle | Iqbal Ahmad Ahmad Almutlg Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method Axioms algorithms escape criteria Julia sets iterative methods generalized rational functions |
| title | Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method |
| title_full | Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method |
| title_fullStr | Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method |
| title_full_unstemmed | Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method |
| title_short | Generation of Julia Sets for a Novel Class of Generalized Rational Functions via Generalized Viscosity Iterative Method |
| title_sort | generation of julia sets for a novel class of generalized rational functions via generalized viscosity iterative method |
| topic | algorithms escape criteria Julia sets iterative methods generalized rational functions |
| url | https://www.mdpi.com/2075-1680/14/4/322 |
| work_keys_str_mv | AT iqbalahmad generationofjuliasetsforanovelclassofgeneralizedrationalfunctionsviageneralizedviscosityiterativemethod AT ahmadalmutlg generationofjuliasetsforanovelclassofgeneralizedrationalfunctionsviageneralizedviscosityiterativemethod |