Multicorn Sets of z¯k+cm via S-Iteration with h-Convexity

Abstract

Fractals represent important features of our natural environment, and therefore, several scientific fields have recently begun using fractals that employ fixed-point theory. While many researchers are working on fractals (i.e., Mandelbrot and Julia sets), only a very few have focused on multicorn sets and their dynamic nature. In this paper, we study the dynamics of multicorn sets of z¯k+cm, where k≥2, c≠0∈C, and m∈R, by using S-iteration with h-convexity instead of standard S-iteration. We develop escape criterion z¯k+cm for S-iteration with h-convexity. We analyse the dynamical behaviour of the proposed conjugate complex function and discuss the variation of iteration parameters along with function parameter m. Moreover, we discuss the effects of input parameters of the proposed iteration and conjugate complex functions of the behaviour of multicorn sets with numerical simulations.

Escape Criteria Using Hybrid Picard S-Iteration Leading to a Comparative Analysis of Fractal Mandelbrot Sets Generated with S-Iteration

“…People interested in designing aesthetically pleasing patterns will find great satisfaction in the findings of this paper. For further future applications, this work can be combined with [52,53]. In future, comparisons can be made with other iterations and the process can be improved for higher-order polynomials and transcendental functions.…”