Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with [formula omitted]-convexity

Abstract

In this paper, we introduce a generalized rational map to develop a theory of escape criterion via the SP-iteration process equipped with s-convexity. Furthermore, we develop algorithms for the exploration of unique kinds of Mandelbrot as well as Julia sets. We demonstrate graphically the change in colour, size, and shape of images with the change in values of the considered iteration’s parameters. The new fractals thus obtained are visually very pleasing and attractive. Most of these newly generated fractals resemble natural objects around us. Moreover, we numerically study the dependence between the iteration’s parameters and the set size. The experiments show that this dependency is non-linear. We believe that the obtained conclusions will motivate researchers who are interested in fractal geometry.