Complex Dynamics of Ishikawa Iterates for Non Integer Values

Abstract

We explore in this paper the dynamics of the complex function for non integer values, using the Ishikawa iterates. The z plane fractal images are studied for positive powers of the complex function while c plane fractals are analyzed for negative powers of the complex function.

Generation of Julia and Mandelbrot Sets via Fixed Points

“…In 2010, a two-step Ishikawa iteration was used by Rana and Kumar [20] and Chauhan et al [21] to study relative superior Julia and relative superior Mandelbrot sets, respectively. The dynamics of the nth order complex polynomial for non integer values were investigated in [22]. The authors also obtained new Julia and Mandelbrot sets via Ishikawa orbit.…”

Transcendental Picard-Mann hybrid Julia and Mandelbrot sets

“…For a complete literature review of superior fractals until 2010, one may refer to Singh, Mishra and Sinkala [18]. In 2010, Chauhan, Rana and Negi [5] obtained relative Julia and Mandelbrot sets via Ishikawa iterates. Ashish, Rani and Chugh [4] visualized new Julia sets and Mandelbrot sets in Noor orbit [10].…”

New Fixed Point Results for Fractal Generation in Jungck Noor Orbit withs-Convexity

“…Julia and Mandelbrot sets have been studied under the effect of noises [1][2][3][4] arising in the objects. In 1982, Mandelbrot [2] introduced superior iterates (a two-step feedback process) in the study of fractal theory and created superior Julia and Mandelbrot sets.…”

“…Negi and Rani [6] simulated the behavior of Julia sets using switching processes. Chauhan et al [4] obtained new Julia and Mandelbrot sets via Ishikawa iterates (an example of three-step feedback process). Kang et al [8] introduced Julia and Mandelbrot sets in Jungck Mann and Jungck Ishikawa orbits.…”