New Julia and Mandelbrot sets for a new faster iterative process

Abstract

Fixed point iterative procedures are the backbones of fractal geometry. In existing literature Julia sets, Mandelbrot sets and their variants have been studied using one - step, two - step, three - step and four - step iterative process. Recently, M. Abbas and T. Nazir [12] introduced a new iterative process (a four-step iterative process) which is faster than all of Picard, Mann and Agarwal processes. In this paper, we obtain further generalizations of Julia and Mandelbrot sets using this faster iterative process for quadratic, cubic and higher degree polynomials. Further, we analyze that few Julia and Mandelbrot sets took the shape of Lord Ganesha (name of Hindu God), Dragon and Urn.