The Research on Anti-counterfeiting of Fractal Graphics in Color Printing Based on Escape Time Algorithm of Julia-set

2011 ◽  
pp. 174-179
Author(s):  
Fucheng You ◽  
Yingjie Liu
Keyword(s):  
Julia Set ◽  
Time Algorithm ◽  
Escape Time ◽  
Color Printing

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.

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

2021 ◽  
Vol 5 (2) ◽  
pp. 55
Author(s):  
Yang Zhao ◽  
Shicun Zhao ◽  
Yi Zhang ◽  
Da Wang
Keyword(s):  
Julia Set ◽  
Julia Sets ◽  
Initial Point ◽  
Visual Display ◽  
Time Algorithm ◽  
Escape Time ◽  
Polynomial Maps ◽  
Distribution Rule ◽  
Connected Area ◽  
Criterion Method

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.

scholarly journals Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods

2001 ◽  
Vol 28 (9) ◽  
pp. 545-548
Author(s):  
Anna Tomova
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Set Theory ◽  
Julia Set ◽  
Time Algorithm ◽  
Escape Time ◽  
Special Cases ◽  
Problems And Solutions ◽  
The One

In 1977 Hubbard developed the ideas of Cayley (1879) and solved in particular the Newton-Fourier imaginary problem. We solve the Newton-Fourier and the Chebyshev-Fourier imaginary problems completely. It is known that the application of Julia set theory is possible to the one-dot numerical method like the Newton's method for computing solution of the nonlinear equations. The secants method is the two-dots numerical method and the application of Julia set theory to it is not demonstrated. Previously we have defined two one-dot combinations: the Newton's-secants and the Chebyshev's-secants methods and have used the escape time algorithm to analyse the application of Julia set theory to these two combinations in some special cases. We consider and solve the Newton's-secants and Tchebicheff's-secants imaginary problems completely.

Pattern Generation Based on Julia Set and its Application in the Design of Seamless Underwear Products

2011 ◽  
Vol 332-334 ◽  
pp. 702-705
Author(s):  
Li Chen ◽  
Rui Zhang
Keyword(s):  
Julia Set ◽  
Time Algorithm ◽  
Pattern Generation ◽  
Escape Time ◽  
Knitted Fabric ◽  
Image Generation ◽  
Pattern Design ◽  
Design Capacity ◽  
Fractal Image

In order to improve the design capacity of knitted fabric pattern and explore new design thought, this article studies the fractal image generation of Julia set and applies it into the pattern design of seamless underwear products. It adopts VB programming to generate Julia set pattern based on escape time algorithm, and then uses part imaging and amplification or changes the function orders to get a lot of colorful patterns. When these generated patterns are imported under the help of Photon software, color part in the patterns will be replaced with pre-designed fabric patterns and finally comes with patterns identifiable to seamless underwear knitting machine. Such method greatly expands the design thoughts of seamless underwear products.

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

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
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