Control of Dynamic Noise in Transcendental Julia and Mandelbrot Sets by Superior Iteration Method

Control of Dynamic Noise in Transcendental Julia and Mandelbrot Sets by Superior Iteration Method

Ketan Jha, Mamta Rani
Copyright: © 2018 |Pages: 12
DOI: 10.4018/IJNCR.2018040104
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Abstract

Researchers and scientists are attracted towards Julia and Mandelbrot sets constantly. They analyzed these sets intensively. Researchers have studied the perturbation in Julia and Mandelbrot sets which is due to different types of noises, but transcendental Julia and Mandelbrot sets remained ignored. The purpose of this article is to study the perturbation in transcendental Julia and Mandelbrot sets. Also, we made an attempt to control the perturbation in transcendental sets by using superior iteration method.
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2. Preliminaries

The generation of transcendental Mandelbrot set is very similar to the Mandelbrot set obtained from standard quadratic equation. The transcendental Julia and Mandelbrot sets are obtained from following equation:

IJNCR.2018040104.m01
(1) where z, cIJNCR.2018040104.m02 C (set of complex numbers) (cf. 2012). Researchers have given the concept of creating cubic and biquadratic transcendental Julia and Mandelbrot sets using superior iterates (2012). Bharti et al. (2017) generated transcendental Julia and Mandelbrot sets in Noor orbit.

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