scholarly journals Anti Mandelbrot Sets via Jungck-M Iteration

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 194663-194675
Author(s):  
Hengxiao Qi ◽  
Muhammad Tanveer ◽  
Muhammad Shoaib Saleem ◽  
Yuming Chu
Keyword(s):  
Mandelbrot Sets

A Study on Mandelbrot Sets to Generate Visual Aesthetic Fractal Patterns

2013 ◽  
Vol 311 ◽  
pp. 111-116 ◽  
Author(s):  
Zong Wen Cai ◽  
Artde D. Kin Tak Lam
Keyword(s):  
Information System ◽  
Program Development ◽  
Development Program ◽  
Visual Basic ◽  
Time Algorithm ◽  
Mandelbrot Set ◽  
Escape Time ◽  
Mandelbrot Sets ◽  
Fractal Patterns ◽  
Power Orders

The fractal pattern is a highly visual aesthetic image. This article describes the generation method of Mandelbrot set to generate fractal art patterns. Based on the escape time algorithm on complex plane, the visual aesthetic fractal patterns are generated from Mandelbrot sets. The generated program development, a pictorial information system, is integrated through the application of Visual Basic programming language and development integration environment. Application of the development program, this article analyzes the shape of the fractal patterns generated by the different power orders of the Mandelbrot sets. Finally, the escape time algorithm has been proposed as the generation tools of highly visual aesthetic fractal patterns.

scholarly journals is regular-closed

2018 ◽  
Vol 40 (1) ◽  
pp. 213-220 ◽  
Author(s):  
YUTARO HIMEKI ◽  
YUTAKA ISHII
Keyword(s):  
Rotational Symmetry ◽  
Iterated Function Systems ◽  
Geometric Proof ◽  
Contraction Ratio ◽  
Iterated Function ◽  
Mandelbrot Sets ◽  
Self Similar ◽  
Regular Closed

For each $n\geq 2$, we investigate a family of iterated function systems which is parameterized by a common contraction ratio $s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s|<1\}$ and possesses a rotational symmetry of order $n$. Let ${\mathcal{M}}_{n}$ be the locus of contraction ratio $s$ for which the corresponding self-similar set is connected. The purpose of this paper is to show that ${\mathcal{M}}_{n}$ is regular-closed, that is, $\overline{\text{int}\,{\mathcal{M}}_{n}}={\mathcal{M}}_{n}$ holds for $n\geq 4$. This gives a new result for $n=4$ and a simple geometric proof of the previously known result by Bandt and Hung [Fractal $n$-gons and their Mandelbrot sets. Nonlinearity 21 (2008), 2653–2670] for $n\geq 5$.

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

2018 ◽  
Vol 7 (2) ◽  
pp. 48-59 ◽  
Author(s):  
Ketan Jha ◽  
Mamta Rani
Keyword(s):  
Iteration Method ◽  
Dynamic Noise ◽  
Different Types ◽  
Mandelbrot Sets

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.

scholarly journals Fixed point results in the generation of Julia and Mandelbrot sets

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Waqas Nazeer ◽  
Shin Min Kang ◽  
Muhmmad Tanveer ◽  
Abdul Aziz Shahid
Keyword(s):  
Fixed Point ◽  
Mandelbrot Sets

Generalized baby Mandelbrot sets adorned with halos in families of rational maps

2016 ◽  
Vol 23 (3) ◽  
pp. 503-520 ◽  
Author(s):  
HyeGyong Jang ◽  
YongNam So ◽  
Sebastian M. Marotta
Keyword(s):  
Rational Maps ◽  
Mandelbrot Sets

scholarly journals Smooth Decomposition of Generalized Fatou Set Explains Smooth Structure in Generalized Mandelbrot Set

1988 ◽  
Vol 43 (1) ◽  
pp. 14-16 ◽  
Author(s):  
J. Peinke ◽  
J. Parisi ◽  
B. Röhricht ◽  
O. E. Rössler ◽  
W. Metzler
Keyword(s):  
Parameter Space ◽  
Initial Conditions ◽  
Logistic Map ◽  
Mandelbrot Set ◽  
Fatou Set ◽  
Smooth Structure ◽  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

Abstract Generalized Mandelbrot sets arise in perturbed (non-analytic) versions of the complex logistic map. Numerically, it contains smooth portions as shown previously. To exclude that this result is specific to particular initial conditions only, the structure of the analogue to the Fatou set is looked at in the region in question. The set of non-divergent points is being "eaten up" by a smooth invading boundary. Therefore, the same type of decomposition applies independent of position in parameter space, in the region in question.

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