Construction of fractals with Picard-CR iteration equipped with s-convexity for a complex rational function

Abstract

Fractal sets like Julia set and Mandelbrot set are generated through iterative function systems. Our study proposes Picard--CR iteration equipped with s-convexity to generate some derivatives of Julia and Mandelbrot fractals for a complex rational function $a z^{m}+\frac{b}{z^{n}}+c$ where $m,n\in\mathbb{N}$, $a,b,c\in\mathbb{C}$, $m\geq2$ and $|a|\geq1$. The escape criterion for our proposed iterative scheme is derived via the complex rational function. We investigate how alterations in parameters influence fractals structures. The graphical depictions are scrutinized to verify alterations.