Noise-perturbed quaternionic Mandelbrot sets

Sun, Yaqi; Wang, X. Y.

doi:10.1080/00207160903131228

Cited by 11 publications

(2 citation statements)

References 28 publications

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“…By distinguishing the points with different colors according to the different strike frequency, the reference [21] presented an equipotential point algorithm to construct the Julia sets. Moreover, some research has been done to investigate the algorithm for constructing 3D M-J sets [22][23][24]. With the help of the ETA, some other related problems about the fractal have also been effectively analyzed and addressed.…”

Section: Introductionmentioning

confidence: 99%

On the Connectivity Measurement of the Fractal Julia Sets Generated from Polynomial Maps: A Novel Escape-Time Algorithm

Zhao

Zhang

et al. 2021

Fractal Fract

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In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of Julia sets. For the quantitative part, a connectivity criterion method is designed by exploring the distribution rule of the connected regions, with an output value Co in the range of [0,1]. The smaller the Co value outputs, the better the connectivity is. For the visual part, we modify the classical escape-time algorithm by highlighting and separating the initial point of each connected area. Finally, the Julia set is drawn into different brightnesses according to different Co values. The darker the color, the better the connectivity of the Julia set. Numerical results are included to assess the efficiency of the algorithm.

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Section: Introductionmentioning

confidence: 99%

On the Connectivity Measurement of the Fractal Julia Sets Generated from Polynomial Maps: A Novel Escape-Time Algorithm

Zhao

Zhang

et al. 2021

Fractal Fract

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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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