General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group

K.W. Chung; H.S.Y. Chan; N. Chen

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General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group

机译：来自模块组等变映射的具有颜色对称性的通用Mandelbrot集和Julia集

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A method for constructing the general M (Mandelbrot) set of a non-analytic mapping is presented. The equivariant mapping with symmetry of the modular group is considered as an illustration. By investigating the distribution of attractors in the upper half-plane and the assignment of colors to each attractor, an algorithm is presented for the construction of filled-in Julia sets with 2- or 3-color symmetry. Such Julia sets not only reveal the characteristics of a system, but also have high artistic appeal.

机译：提出了一种用于构造非解析映射的一般M（Mandelbrot）集的方法。具有模块化的对称性的等变映射被认为是说明。通过研究上半平面吸引子的分布以及每个吸引子的颜色分配，提出了一种算法，用于构造具有2或3色对称性的填充Julia集。这样的茱莉亚布景不仅揭示了系统的特征，而且具有很高的艺术吸引力。

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来源
《Computers & Graphics》 |2000年第6期|p.911-918|共8页
作者
K.W. Chung; H.S.Y. Chan; N. Chen;
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作者单位

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类一般性问题;计算机的应用;
关键词
Chaos; Equivariant mapping; Mandelbrot set; Julia set; Color symmetry;

机译：混沌;等变映射;Mandelbrot套装;朱莉娅套装;颜色对称;

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专利

1. General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group [J] . K.W. Chung, H.S.Y. Chan, N. Chen Computers & Graphics . 2000,第6期

机译：来自模块组等变映射的具有颜色对称性的通用Mandelbrot集和Julia集
2. General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group [J] . K.W. Chung, H.S.Y. Chan, N. Chen Computers & Graphics . 2000,第6期

机译：Mandelbrot Sets和Julia套装与模块化组的等意大动映射的颜色对称
3. RESEARCH ON BROWNIAN MOVEMENT BASED ON GENERALIZED MANDELBROT–JULIA SETS FROM A CLASS COMPLEX MAPPING SYSTEM [J] . XINGYUAN WANG, WEI LIU, XUEJING YU Modern Physics Letters, B. Condensed Matter Physics, Statistical Physics, Applied Physics . 2007,第20期

机译：一类复杂映射系统基于广义Mandelbrot-Juliia集的布朗运动研究
4. Fractal Structures of General Mandelbrot Sets and Julia Sets Generated From Complex Non-Analytic Iteration F_m (z) = z~m + C [C] . Yan Dejun, Wei Xiaodan, Zhang Hongpeng, International Symposium on Computer, Communication, Control and Automation . 2013

机译：一般Mandelbrot集的分形结构和复杂非分析迭代F_m（z）= z〜m + c产生的Julia集
5. A computer assisted study of dynamical systems, Julia sets, and the Mandelbrot set [D] . Tucker, Linda Henshaw 1992

机译：计算机辅助研究动力系统，朱莉娅集合和曼德尔布罗特集合
6. Review of Fractals and Chaos: The Mandelbrot Set and Beyond by B. Mandelbrot [O] . Alberto Diaspro 2005

机译：B. Mandelbrot撰写的分形与混沌：Mandelbrot集及其之后的评论
7. Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn [O] . Tomoki Kawahira 2020

机译：Zalcman函数和相似性的Mandelbrot Set，Julia Sets和Tricorn

General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group

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