Julia and Mandelbrot Sets of Transcendental Cosine-Function Using Picard-Thakur Iteration Method

Source abstract

Although Julia and Mandelbrot sets have been widely investigated, the geometric and dynamical behavior of transcendental functions under the Picard–Thakur iterative scheme remains insufficiently understood. This study aims to generate and analyze Julia and Mandelbrot sets for transcendental functions and investigate how parameter variations affect their topology. The selected functions were iterated using the Picard–Thakur scheme, and the resulting fractal structures were examined under varying parameter configurations. The findings reveal that parameter adjustments produce substantial transformations in the 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 generated through Picard–Thakur iteration. The study contributes to the understanding of fractal dynamics associated with transcendental functions and offers potential implications for computational mathematics, dynamical systems, and related applied sciences.