Julia and Mandelbrot Sets of Transcendental Cosine-Function Using Picard-Thakur Iteration Method
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247-265
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10.58578/mjaei.v3i2.9408
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Authors:Babawuro Zuwaira1*, Manjak N. H2, Kwami A. M3, Adamu M. Y4, Ismaila O. I5
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Abstract
This study focuses on the generation and analysis of Julia and Mandelbrot sets for transcendental functions using the Picard–Thakur iterative scheme. It aims to examine the fractal structures produced by selected transcendental functions and investigate how parameter variations influence their topology. The study applied the Picard–Thakur iteration to generate fractal patterns and analyzed the resulting structures using the escape criterion. The findings indicate that parameter tuning produces significant transformations in fractal patterns, including the emergence of symmetrical and spiral-like structures. These results demonstrate the geometric complexity and dynamical sensitivity of transcendental Julia and Mandelbrot sets under the Picard–Thakur iterative scheme. The study concludes that the Picard–Thakur iteration provides a useful computational approach for exploring the behavior of fractal sets associated with transcendental functions. This research contributes to computational mathematics and dynamical systems by offering deeper insight into parameter-dependent fractal formation, with potential relevance to applied sciences involving nonlinear and complex dynamical structures.
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References
Amobeda, R. E., Aboiyar, T., Adee, S. O., & Ayoo, P. V. (2016). Julia and Mandelbrot sets of the gamma function using Lanczos approximation. Applied and Computational Mathematics, 5(2), 73–77. https://doi.org/10.11648/j.acm.20160502.16
Babawuro, Z., Manjak, N. H., Abba, A. S., Adam, H. Z., & Ibrahim, M. (2022). On Julia and Mandelbrot sets of gamma and beta functions for fractal images. Science Forum (Journal of Pure and Applied Sciences), 22(2), 227–233. https://bibliomed.org/?mno=127200
Barnsley, M. F. (1993). Fractals everywhere (2nd ed.). Academic Press.
Bhoria, A., Panwar, A., & Sajid, M. (2023). Mandelbrot and Julia sets of transcendental functions using Picard–Thakur iteration. Fractal and Fractional, 7(10), Article 768. https://doi.org/10.3390/fractalfract7100768
Blankers, V., Rendfrey, T., Shukert, A., & Shipman, P. D. (2019). Julia and Mandelbrot sets for dynamics over the hyperbolic numbers. Fractal and Fractional, 3(1), Article 6. https://doi.org/10.3390/fractalfract3010006
Brouers, F., & Sotolongo-Costa, O. (2006). Generalized fractal kinetics in complex systems: Application to biophysics and biotechnology. Physica A: Statistical Mechanics and Its Applications, 368(1), 165–175. https://doi.org/10.1016/j.physa.2005.12.062
Danca, M.-F. (2024). Mandelbrot set as a particular Julia set of fractional order, equipotential lines and external rays of Mandelbrot and Julia sets of fractional order. Fractal and Fractional, 8(1), Article 69. https://doi.org/10.3390/fractalfract8010069
Danca, M.-F., & Fečkan, M. (2023). Mandelbrot set and Julia sets of fractional order. Nonlinear Dynamics, 111(10), 9555–9570. https://doi.org/10.1007/s11071-023-08311-2
Hardy, H. H., & Beier, R. A. (1994). Fractals in reservoir engineering. World Scientific.
Julia, G. (1918). Mémoire sur l’itération des fonctions rationnelles. Journal de Mathématiques Pures et Appliquées, 8(1), 47–245.
Losa, G. A., Merlini, D., Nonnenmacher, T. F., & Weibel, E. R. (Eds.). (2002). Fractals in biology and medicine (Vol. 3). Birkhäuser.
Mandelbrot, B. B. (1975). Les objets fractals: Forme, hasard et dimension. Flammarion.
Thompson, A. H. (1991). Fractals in rock physics. Annual Review of Earth and Planetary Sciences, 19, 237–262. https://doi.org/10.1146/annurev.ea.19.050191.001321
Tomar, A., Kumar, V., Rana, U. S., & Sajid, M. (2023). Fractals as Julia and Mandelbrot sets of complex cosine functions via fixed point iterations. Symmetry, 15(2), Article 478. https://doi.org/10.3390/sym15020478
Zou, C., Shahid, A. A., Tassaddiq, A., Khan, A., & Ahmad, M. (2020). Mandelbrot sets and Julia sets in Picard–Mann orbit. IEEE Access, 8, 64411–64421. https://doi.org/10.1109/ACCESS.2020.2984689