Generation of Fractals and Antifractals Via DK Iteration

Abstract

 A fractal is a complex mathematical pattern constructed from simple repetitive forms that shrink in size with each repetition. The purpose of this research is to identify escape criteria for complex polynomials $Q_c(p) = p^k + c $ and anti polynomials $A_c(p) = \overline{p}^k + c,$ where $c \in \mathbb{C}$ and $k \geq 2,$ respectively, to generate fractals (Julia and Mandelbrot sets) and antifractals (anti Julia sets and anti Mandelbrot sets) using DK fixed point iterative procedure. Fractal geometry has been studied, and stunning artistic creations have been produced as a result.