Fractals Patterns as Mandelbrot Sets for a Complex Functions via Viscosity Approximation Iterative Method

Abstract

This article explores novel fractal patterns within Mandelbrot sets generated by a new class of complex functions of the forms and , where p ≥ 2, ϑ, ,  and , where the traditional constant term is replaced with a logarithmic function. Utilizing a viscosity approximation-type iterative method, we develop escape criteria that enhance existing algorithms and enable the effective visualization of intricate Mandelbrot sets. Our findings reveal dynamic transformations in the shape and size of these fractals as key input parameters are varied. We believe that the insights gained from this study will inspire and motivate researchers and enthusiasts with a deep interest in fractal geometry.