New Julia and Mandelbrot Sets for Jungck Ishikawa Iterates

TL;DR

This paper introduces new fractal sets called Relative Superior Mandelbrot and Julia sets generated through Jungck Ishikawa Iteration applied to polynomial dynamics, expanding the understanding of fractal generation methods.

Contribution

It presents a novel application of Jungck Ishikawa Iteration to generate new classes of fractals, specifically Relative Superior Mandelbrot and Julia sets, for polynomial functions.

Findings

Generated new types of Mandelbrot and Julia sets.

Applied Jungck Ishikawa Iteration to polynomial dynamics.

Provided mathematical framework for fractal generation.

Abstract

The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z^ n - z + c = 0 for n>=2 and applied Jungck Ishikawa Iteration to generate new Relative Superior Mandelbrot sets and Relative Superior Julia sets. In order to solve this function by Jungck type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = z^ n + c and Sz = z. Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for polynomials in the literature but in this paper we have generated Relative Mandelbrot sets and Relative Julia sets.