An application of nonstandard viscosity iterative methods with s-convexity in the generation of fractals for rational maps

This paper introduces an application of novel fractal patterns, specifically Julia and Mandelbrot sets, generated by a modified class of complex rational maps in which the traditional constant term is replaced with a logarithmic component. By utilizing nonstandard viscosity iterative methods with s-convexity, we derive enhanced escape criteria that refine existing computational algorithms, thereby enabling the precise visualization of intricate fractal structures as Julia and Mandelbrot sets. Our results demonstrate dynamic transformations in the shape and size of these fractals as key input parameters are adjusted. We believe that the insights garnered from this research will inspire and motivate researchers and enthusiasts deeply engaged in the field of fractal geometry.