Julia and Mandelbrot Sets of Transcendental Cosine-Function Using Picard-Thakur Iteration Method - Babawuro Zuwaira; Manjak N. H; Kwami A. M; Adamu M. Y; Ismaila O. I (Darul Yasin Al Sys, 2026)
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.