Generation of fractals and antifractals via Picard S Iteration

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.