Variants of Mandelbrot and Julia fractals for higher‐order complex polynomials

Abstract

We establish some escape criteria via Jungck–Mann fixed point iteration system with ‐convexity for complex‐valued polynomials of higher orders. As a result, we point out errors in the corresponding existing criterion and develop a correct technique to obtain the escape criterion for analogous fixed point iterations equipped with ‐convexity. Further, we derive a novel escape radius for visualizing the alluring fractals. Toward the end, we utilize our conclusions to generate some variants of classical Mandelbrot and Julia sets. We observe that the visualized fractals are similar to beautiful objects found in nature and each point in Mandelbrot set includes a massive image data of a Julia set. Some examples are also provided to demonstrate the variation in images and discuss the impact of parameters on the deviation of color and appearance of fractals.