华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (1): 30-36.

• 数学 统计学 • 上一篇    下一篇

复动力系统生成循环群和二面体群对称图像

邹玉茹1, 鲁坚2   

  1. 1. 华东师范大学 数学系, 上海 200062; 2. 上海交通大学 数学系, 上海 200240;
  • 收稿日期:2007-02-28 修回日期:2007-03-19 出版日期:2008-01-25 发布日期:2008-01-25
  • 通讯作者: 邹玉茹

Images with cyclic or dihedral symmetry generatedby complex dynamical (Chinese)systems

ZOU Yu-ru1, LU Jian2   

  1. 1. Department of Mathematics,East China Normal University, Shanghai 200062,China; 2. Department of Mathematics, Shanghai Jiaotong Univesity, Shanghai 200240, China
  • Received:2007-02-28 Revised:2007-03-19 Online:2008-01-25 Published:2008-01-25

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摘要： 探讨了从动力系统角度生成具有循环群和二面体群对称性图像的轨迹井方法，并给出了构造对称轨迹井的理论依据.构造具有Cn和Dn对称性的函数作为迭代函数系统，对生成的点序列进行轨迹井跟踪，同时结合调色板技术提出一种新的绘色算法，生成具有很强艺术效果的Cn和Dn对称性图像.

关键词: 循环群对称, 二面体群对称, 混沌, 动力系统, 循环群对称, 二面体群对称, 混沌, 动力系统

Abstract: This paper explored the orbit trap methods for generating images with cyclic or dihedral symmetry from a dynamical system's point of view, and illustrated the mathematical principles of the construction of the symmetric orbit traps. Constructing the function with Cn or Dn symmetry, tracking the series of points corresponding to the function and introducing a new coloring algorithm derived from colormap technique, visually fascinating images with Cn or Dn symmetry can be created.

Key words: dihedral symmetry, chaos, dynamical system, cyclic symmetry, dihedral symmetry, chaos, dynamical system

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