Dynamic noise perturbed generalized superior Mandelbrot sets

Agarwal, Rakesh; Agarwal, Vishal

doi:10.1007/s11071-011-0115-2

Cited by 16 publications

(9 citation statements)

References 32 publications

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“…We have shown for a range of SNR values (e.g. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], the parameter estimates are satisfactorily close and that can further improve the system approximations through the mentioned noise reduction techniques.…”

Section: Resultsmentioning

confidence: 99%

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Parameter estimation for 1D PWL chaotic maps using noisy dynamics

et al. 2018

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Many physical situations involve chaotic systems implemented in hardware. Among them onedimensional piecewise linear maps are popular candidates for such applications because of their property of generating robust chaos. In physical implementations, the control parameter of these maps may deviate from its ideal value due to hardware imprecision. Since the dynamics of a chaotic map is completely defined by its control parameter, one needs to know the value of the parameter in a hardware realisation. In this paper, we show that it is possible to determine the parameter, through the realisation of the unstable fixed point of the map, by utilising noise that is always present in the system. We present this in the form of an algorithm and demonstrate its efficacy through simulated results. We also determine the bounds on the signal-to-noise ratio required for successful parameter estimation. The proposed approach is expected to be beneficial to the existing noise reduction techniques and time series recovery algorithms that require a reasonably accurate knowledge of the map.

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Section: Resultsmentioning

confidence: 99%

“…Many studies have been conducted to broadly understand the effect of noise on the chaotic dynamics [16][17][18]. Noise and chaotic trajectories are both wideband signals; therefore, linear filtering techniques (e.g.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

et al. 2018

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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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“…Recently, the attention of scientists has focused on the use of different iteration schemes from fixed point theory in the generation of patterns. The iteration schemes have been mainly used in the generation of fractal patterns defined in the complex plane, such as the well‐known Mandelbrot and Julia sets [AA12, ARC14, RA10], and in polynomiography [GKL15] (a method that is based on the root‐finding methods of complex polynomials).…”

Section: Introductionmentioning

confidence: 99%

Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns

Gdawiec

2015

Computer Graphics Forum

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In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called q‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems—which is similar to the inversion fractals generation algorithm—the proposed generalizations do not give interesting results.

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Dynamic noise perturbed generalized superior Mandelbrot sets

Cited by 16 publications

References 32 publications

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

New Julia and Mandelbrot Sets for a New Faster Iterative Process

Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns

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