Generation of fractals and antifractals via Picard S Iteration

Geeta Biban; Renu Chugh; Sudesh Kumar; Anju Panwar; Amit Kumar

Geeta Biban Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
Renu Chugh Department of Mathematics, Gurugram University, Gurugram 122003, India
Sudesh Kumar Department of Mathematics, Government College for Girls Sector 14, Gurugram 122001, India
Anju Panwar Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
Amit Kumar Maharshi Dayanand University, Rohtak

Abstract

The aim of this paper is to find escape criteria to generate fractals (Julia and Mandelbrot sets) and anti-fractals (anti-Julia sets, tricorns and multicorns) for the complex polynomials $Q_{c}(p)=p^{k}+c$ and antipolynomials $A_{c}(p)=\bar{p}^{k}+c$ where $c\in \mathbb{C}$ and $k\geq2\,$, respectively, by using Picard S iteration scheme. The geometry of fractals has been explored and various wonderful aesthetic designs have been generated.