Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c via Jungck four-step iterative method with s -convexity as well as four-step iterative method

Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c

Abstract

In this manuscript, we explore some new stunning fractals of Julia sets by developing the escape criteria for novel type of complex function $ p(z) = a \exp[d\sin(z^n)]- bz + c,$ where $n,|d|\geq 2$ and $a,b,c,d\in\mathbb{C}$ and furnish some graphical illustrations of the generated amazing fractals, utilizing the Jungck four-step iteration scheme equipped with $s$-convexity as well as four-step iteration scheme. Moreover, we conclude this work by examining variation in images and the impact of parameters on the deviation of dynamics, color, and appearance of fractals. At some fixed input parameters, we observe the engrossing behavior of Julia sets for different $n.$