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Distributional escape time algorithm Based on Generalized Fractal Sets in Cloud Environment

Chinese Journal of Electronics 2015年第1期24卷 124-127页

作者： LIU Miao LIU Shuai FU Weina ZHOU Jiantao College of Computer Science and Technology Jilin University College of Computer Inner Mongolia University School of Physical Science and Technology Inner Mongolia University

Since fractal is widely used in all science domains today, escape time algorithm, which is the most effective algorithm in drawing fractal figures, shows negatively when generation function is complex. In this paper,we improve classic escape time algorithm into cloud environment to improve its performance. At first, we provide a separation method of escape algorithm in cloud environment. Then we calculate complexity of the novel algorithm with a probability model based on allocation policy. At last, we use generalized fractal sets as experimental subjects to validate our conclusion. Experimental results show correctness and rapidness of the novel algorithm.

关键词： escape time algorithm Fractal Distribution probability model Cloud environment.

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The Research on Anti-counterfeiting of Fractal Graphics in Color Printing Based on escape time algorithm of Julia-set

The Research on Anti-counterfeiting of Fractal Graphics in C...

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International Conference on Advanced Research on Computer Education, Simulation and Modeling

作者： You, Fucheng Liu, Yingjie Beijing Inst Graph Commun Informat & Mech Engn Sch Beijing 102600 Peoples R China

ISBN: (纸本)9783642217821

Fractal graphics based on escape time algorithm of Julia-set are studied in the paper for the application of anti-counterfeiting in color printing. Different parameters of Julia-set make anti-counterfeiting space difficult to search. Therefore anti-counterfeiting in color printing based on Julia-set is implemented. A novel approach of anti-counterfeiting space based on color and shape is proposed for anti-counterfeiting in color printing. This approach is applied to analyze anti-counterfeiting capacity of fractal graphics based on Julia-set. Firstly, anti-counterfeiting space of RGB color is estimated from fractal graphics of Julia-set. Anti-counterfeiting space is generated on basis of RGB color and graph size. Then, anti-counterfeiting space of shape which is generated by parameters changing enlarges anti-counterfeiting space based on fractal graphics of Julia-set. Different parameters lead to different shape of fractal graphics to a great extent. Experimental results demonstrate that higher anti-counterfeiting capacity of color printing can be achieved with the proposed approach.

关键词： Julia-set escape time algorithm fractal graphics anti-counterfeiting in color printing

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The Application Research on Anti-counterfeiting of Fractal Graphics in Color Printing Based on Newton Iteration and escape time algorithm

The Application Research on Anti-counterfeiting of Fractal G...

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International Conference on Advanced Research on Computer Education, Simulation and Modeling

作者： You, Fucheng Chen, Yujie Beijing Inst Graph Commun Informat & Mech Engn Sch Beijing 102600 Peoples R China

ISBN: (纸本)9783642217821

The anti-counterfeiting printing which is a branch of feature printing is an anti-counterfeiting technology. Anti-counterfeiting printing technology is a measure which is used to prevent somebody unwarranted from copying, counterfeiting and imitating. Fractal graphics is applied to color printing anti-counterfeiting in this paper because of its protean shape and unpredictable color. The detailed analysis of Julia set escape time algorithm of Newton iterative method shows that the method of color printing anti-counterfeiting combined with fractal graphics has prefect anti-counterfeiting functions. No one can get the same graphics with original picture by common methods of duplicating, scanning, photographing and other measures.

关键词： printing anti-counterfeiting fractal graphics Newton iterative algorithm escape time algorithm

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A study on Julia sets to generate visual aesthetic fractal patterns

A study on Julia sets to generate visual aesthetic fractal p...

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2nd International Conference on Innovation, Communication and Engineering (ICICE)

作者： Lam, Artde Donald Kin-Tak She, Guo-Fu Lin, Zhi-Qiang Cai, Zong-Wen Fuzhou Univ Sch Arts & Design Xiamen Xiamen Fujian Peoples R China Fuzhou Univ Inst Creat Ind Res Fuzhou Fujian Peoples R China Earthquake Adm Fujian Prov Xiamen Fujian Peoples R China

ISBN: (纸本)9781315815732;9781138001176

Application of Fractal geometry theory, Fractal patterns can get some special lines and shapes. Comparison of Fractal pattern and the traditional pattern, the Fractal pattern is a highly visual aesthetic image. In this paper, based on the theory of Julia sets, the generation of Fractal patterns has been studied. First of all, the relationship between the Fractal pattern and mathematical morphology parameters has been discussed, escape time algorithm is used to generate Fractal patterns. Then, based on the different power orders of the Julia sets, a computer program has been development to generate Fractal patterns. Finally, the patterns which are generated by the developed program can be applied to the highly visual aesthetic Fractal pattern design.

关键词： Fractal patterns Julia sets escape time algorithm visual aesthetic image

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A Study on Mandelbrot Sets to Generate Visual Aesthetic Fractal Patterns

A Study on Mandelbrot Sets to Generate Visual Aesthetic Frac...

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International Conference on Information, Communication and Engineering (ICICE 2012)

作者： Cai, Zong-Wen Lam, Artde D. Kin-Tak Earthquake Adm Fujian Prov Xiamen Fujian Peoples R China Fuzhou Univ Coll Phys & Informat Engn Fuzhou Fujian Peoples R China

ISBN: (纸本)9783037856727

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.

关键词： Fractal Patterns Mandelbrot Sets escape time algorithm Visual Aesthetic Image

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

Pattern Generation Based on Julia Set and Its Application in...

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International Conference on Textile Engineering and Materials (ICTEM 2011)

作者： Chen, Li Zhang, Rui Tianjin Polytech Univ Sch Text Tianjin 300160 Peoples R China Minist Educ China Key Lab Adv Textile Composities Tianjin 300160 Peoples R China

ISBN: (纸本)9783037852415

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.

关键词： Julia set escape time algorithm pattern generation design of seamless underwear products

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A new escape time algorithm of constructing Julia set

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High Technology Letters 2007年第2期13卷 194-197页

作者：袁杰 Li Xiali Hou Zhiling Cao Maosheng School of Mathematics and Computer Science Central University of Nationalities Beijing 100081 P.R.China School of Materials Science and Engineering Beijing Institute of Technology Beijing 100081 P.R.China

escape time algorithm is an effective theoretical algorithm of constructing fractal graphics. The key of this algorithm lies in the construction of escape time function. A new escape time function is presented based on the research of escape time algorithm. An accelerated escape time algorithm is carried out in this paper. The experiments have demonstrated that the new algorithm is not only as precise as the old, but also faster when it is used to construct Julia set.

关键词： fractal escape time algorithm escape time function Julia set

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Fractal art using variations on escape time algorithms in the complex plane

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JOURNAL OF MATHEMATICS AND THE ARTS 2007年第1期1卷 41-45页

作者： Sisson, P. D. Louisiana State Univ Shreveport 1 Univ Pl Shreveport LA 71115 USA

The creation of fractal art is easily accomplished through the use of widely-available software, and little mathematical knowledge is required for its use. But such an approach is inherently limiting and obscures many possible avenues of investigation. This paper explores the use of orbit traps together with a simple escape time algorithm for creating fractal art based on nontrivial complex-valued functions. The purpose is to promote a more direct hands-on approach to exploring fractal artistic expressions. The article includes a gallery of images illustrating the visual effects of function, colour palette, and orbit trap choices, and concludes with suggestions for further experimentation.

关键词： escape time algorithm Fractal Fractal art Dynamical system Orbit trap

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