Julia sets and Mandelbrot sets in Noor orbit

摘要

In recent literature, researchers have generated Julia sets and Mandelbrot sets in Mann and Ishikawa orbits that are examples of two-step and three-step feedback processes respectively. This paper presents further generalization of Julia and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and higher degree polynomials using a Noor orbit, which is a four-step iterative procedure. The graphical images of Julia and Mandelbrot sets have been visualized and certain patterns in Mandelbrot sets have been recognized. It is fascinating to see that a few Mandelbrot sets are akin to a butterfly or a coupled urn or a coupled trident.