Anti Mandelbrot Sets via Jungck-M Iteration

Abstract

Complex fractals achieved the highest popularity in the last ten years. Researchers used the fixed point iterations to visualize the fractals and compared the image generation times to check the efficiencies of iterations. This paper explores the behavior of Jungck-M iteration in the generation of anti-Mandelbrot sets. We define the orbit of Jungck-M iteration and prove its escape criteria. We establish the algorithm for anti-Mandelbrot set and visualize some graphs via proposed iteration. We calculate the image generation times for the generation of anti-Mandelbrot sets in proposed orbit and present the comparison with Jungck-CR iteration. We also discuss the variations in images at different values of the input parameters. Moreover, we present the graphs to show the escape time depends on input parameters.

Generation of Fractals using Polar Coordinates

“…Beginning with the classical studies of Benoit Mandelbrot (1), who expanded on the work of Gaston Julia (2), many researchers have studied Julia sets and Mandelbrot sets from different sides (3)(4)(5)(6)(7)(8). Various generalizations of these sets have been proposed.…”