A new approach to dynamic noise on superior Mandelbrot set

Negi, Ashish; Rani, Mamta

doi:10.1016/j.chaos.2006.07.026

Cited by 42 publications

(17 citation statements)

References 5 publications

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“…This will give the ability of changing a biomorph's shape in a predictable way. Negi et al [20] and Rani et al [26] have made a research on the noise in superior Mandelbrot set and superior Julia sets, so we will try to extend their work on the modified biomorphs introduced in this paper.…”

Section: Discussionmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm. Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant.

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Section: Discussionmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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“…We remark that general noise with λ = 0 is multiplicative noise while general noise with λ = 1 is the additive noise [15]. …”

Section: Generalized Mandelbrot Maps Subject To Noisementioning

confidence: 99%

“…The sequence {z n } constructed in this manner is the superior orbit for the complex-valued function with initial choice z 0 and parameter s, and the same is denoted by SO(f, z 0 , s). For details and to see different superior Mandelbrot sets at different values of s, refer to [15] and [17,19,20]. Rani and Agarwal also studied the effect of stochastic noise on superior Julia sets and found drastic results compared to usual Julia sets [18].…”

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confidence: 99%

Dynamic noise perturbed generalized superior Mandelbrot sets

Agarwal

Agarwal²

2011

Nonlinear Dyn

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The invention of the latest tools and technology toward computer aided graphics and drawing completely change the thinking view of researchers in analyzing and studying the behavior of a dynamical system. Inspired by work already performed and by adopting the experimental mathematical methods of combining the theory of analytic function with computer aided drawing technology, we generated generalized superior Mandelbrot sets (SM-sets). Also, we analyzed the effect of dynamic noise on SM-sets.

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“…Also, they have studied the fractal structure and discontinuity law of the generalized Julia sets generated from the extended complex mapping z n + c, where n ∈ R [25]. Further, Julia and Mandelbrot sets have been studied under the effect of noises [19,4,14,15,27]. In 2004, Rani and Kumar [17,18] introduced the superior iterate and created superior Julia and Mandelbrot sets for quadratic [17,18] and cubic [17,18] polynomials.…”

Section: Introductionmentioning

confidence: 99%

New Julia and Mandelbrot Sets for a New Faster Iterative Process

Kumari¹,

Ashish²,

Chugh³

2016

Int. J. of Pure and Appl. Math.

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Fixed point iterative procedures are the backbones of fractal geometry. In existing literature Julia sets, Mandelbrot sets and their variants have been studied using one -step, two -step, three -step and four -step iterative process. Recently, M. Abbas and T. Nazir[12] introduced a new iterative process (a four-step iterative process) which is faster than all of Picard, Mann and Agarwal processes. In this paper, we obtain further generalizations of Julia and Mandelbrot sets using this faster iterative process for quadratic, cubic and higher degree polynomials. Further, we analyze that few Julia and Mandelbrot sets took the shape of Lord Ganesha (name of Hindu God), Dragon and Urn.

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A new approach to dynamic noise on superior Mandelbrot set

Cited by 42 publications

References 5 publications

Biomorphs via modified iterations

Biomorphs via modified iterations

Dynamic noise perturbed generalized superior Mandelbrot sets

New Julia and Mandelbrot Sets for a New Faster Iterative Process

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