Fuzzy fractal dimension based on escape time algorithm

2014 ◽  
Vol 8 ◽  
pp. 117-129 ◽  
Author(s):  
Nadia M. G. Al-Saidi ◽  
Arkan J. Mohammed ◽  
Adil M. Ahmed
Keyword(s):  
Fractal Dimension ◽  
Time Algorithm ◽  
Escape Time

scholarly journals Performance evolution of a fractal dimension estimated by an escape time algorithm

2019 ◽  
Vol 38 (7) ◽  
pp. 109-124
Author(s):  
Arkan Mohammed
Keyword(s):  
Correlation Function ◽  
Fractal Dimension ◽  
Correlation Dimension ◽  
Function Versus ◽  
Fractal Dimensions ◽  
Time Algorithm ◽  
Escape Time ◽  
Geometric Complexity ◽  
Time Dimension ◽  
Fractal Set

The non-geometric and irregular objects are considered as complex patterns. The geometric complexity is measured as space lling capacity by a factor known as a fractal dimension. Dierent techniques are proposed to nd this complexity measure according to the properties of the pattern. This paper is aimed to introduce a method for counting the dimension of the lled Julia fractal set generated by the Escape Time Algorithm using the method of spreading the points inside the proposed window. The resulted dimension is called Escape Time dimension. A new method to compute a correlation dimension of the Filled Julia fractal set is also proposed based on the Grassberger-Procaccia algorithm by computing the correlation function. A log-log graph of the correlation function versus the distances between every pair of points in the lled Julia fractal set is an approximation of the correlation dimension. Finally, a comparison between these two fractal dimensions of the led Julia fractal set which is generated by the Escape Time Algorithm is presented to show the efficiency of the proposed method.

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.

Distributional Escape Time Algorithm Based on Generalized Fractal Sets in Cloud Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 124-127 ◽  
Author(s):  
Miao Liu ◽  
Shuai Liu ◽  
Jiantao Zhou ◽  
Weina Fu
Keyword(s):  
Time Algorithm ◽  
Escape Time ◽  
Cloud Environment ◽  
Fractal Sets

Generalized J Sets Based on Periodic Orbit and Attract Time

2014 ◽  
Vol 989-994 ◽  
pp. 1806-1809
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Zi Yang Han
Keyword(s):  
Periodic Orbit ◽  
Time Algorithm ◽  
Escape Time

The paper introduces escape-time algorithm applied to construct G-J set firstly, and two methods are presented for generating a great diversity of generalized J sets in which the point fall in low-cycle attract collections in the domain. One of the coloring methods is according to attract time, another is by recording the domain of the orbits. We used frieze group map to validate effectiveness for algorithm.

Improvement of Escape Time Algorithm by No-Escape-Point

2011 ◽  
Vol 6 (8) ◽  
Author(s):  
Shuai Liu ◽  
Xiangjiu Che ◽  
Zhengxuan Wang
Keyword(s):  
Time Algorithm ◽  
Escape Time

COMPOSED ACCELERATED ESCAPE TIME ALGORITHM TO CONSTRUCT THE GENERAL MANDELBROT SETS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 149-153 ◽  
Author(s):  
XIANGDONG LIU ◽  
ZHILIANG ZHU ◽  
GUANGXING WANG ◽  
WEIYONG ZHU
Keyword(s):  
Time Algorithm ◽  
Mandelbrot Set ◽  
Escape Time ◽  
Mandelbrot Sets

In this paper, we present a new composed accelerated escape time algorithm by introducing a new composed iterative function. By the new algorithm, the points in the general Mandelbrot set can be decided rapidly with the same precision of the origin escape time algorithm.

scholarly journals On topological conjugacy of some chaotic dynamical systems on the Sierpinski gasket

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2317-2331
Author(s):  
Nisa Aslan ◽  
Mustafa Saltan ◽  
Bünyamin Demir
Keyword(s):  
Dynamical Systems ◽  
Sierpinski Gasket ◽  
Iterated Function Systems ◽  
Time Algorithm ◽  
Periodic Points ◽  
Topological Conjugacy ◽  
Escape Time ◽  
Sierpiński Gasket ◽  
Iterated Function ◽  
Self Similar

The dynamical systems on the classical fractals can naturally be obtained with the help of their iterated function systems. In the recent years, different ways have been developed to define dynamical systems on the self similar sets. In this paper, we give composition functions by using expanding and folding mappings which generate the classical Sierpinski Gasket via the escape time algorithm. These functions also indicate dynamical systems on this fractal. We express the dynamical systems by using the code representations of the points. Then, we investigate whether these dynamical systems are topologically conjugate (equivalent) or not. Finally, we show that the dynamical systems are chaotic in the sense of Devaney and then we also compute and compare the periodic points.

scholarly journals Fractals Parrondo’s Paradox in Alternated Superior Complex System

2021 ◽  
Vol 5 (2) ◽  
pp. 39
Author(s):  
Yi Zhang ◽  
Da Wang
Keyword(s):  
Complex System ◽  
Julia Set ◽  
Julia Sets ◽  
Time Algorithm ◽  
Mandelbrot Set ◽  
Escape Time ◽  
Parrondo’S Paradox ◽  
The One ◽  
Totally Disconnected ◽  
Superior Mandelbrot Set

This work focuses on a kind of fractals Parrondo’s paradoxial phenomenon “deiconnected+diconnected=connected” in an alternated superior complex system zn+1=β(zn2+ci)+(1−β)zn,i=1,2. On the one hand, the connectivity variation in superior Julia sets is explored by analyzing the connectivity loci. On the other hand, we graphically investigate the position relation between superior Mandelbrot set and the Connectivity Loci, which results in the conclusion that two totally disconnected superior Julia sets can originate a new, connected, superior Julia set. Moreover, we present some graphical examples obtained by the use of the escape-time algorithm and the derived criteria.

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