Estimation of Dynamic Noise in Mandelbrot Map

Estimation of Dynamic Noise in Mandelbrot Map

Ketan Jha, Mamta Rani
Copyright: © 2017 |Pages: 20
DOI: 10.4018/IJALR.2017070101
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Abstract

Julia and Mandelbrot sets have been studied continuously attracting fractal scientists since their creation. As a result, Julia and Mandelbrot sets have been analyzed intensively. In this article, researchers have studied the effect of noise on these sets and analyzed perturbation. Continuing the trend in this article, they analyze perturbation and find the corresponding amount of dynamic noise in the Mandelbrot map. Further, in order to recover a distorted fractal image, a restoration algorithm is presented.
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2. Preliminaries

The quadratic polynomial equation to obtain Mandelbrot map, denoted by Qc is represented by

xn+1= x2n– y2n+ c1 and yn+1= 2xnyn+ c2(1)

where, c1, c2 ϵ R (reals).

Argyris et al. (2000) gave two parameters m1 and m2 for perturbation in the Mandelbrot map, and is defined as:

xn+1= x2n– y2n+ c1 + m1wn and yn+1= 2xnyn+ c2 + m2wn(2)

where, c1, c2 ϵ R, wn is a noise vector and m1 and m2 are the parameters designating strength of additive noise. Argyris et al. (2000) had another two parameters k1 and k2 for perturbation in the Mandelbrot map, which is defined as:

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