[1]陈 露.动力系统双曲对称的高效生成方法[J].南京师范大学学报(工程技术版),2014,14(01):076-81.
　Chen Lu.Efficiently Generating Hyperbolic Symmetries of Dynamic Systems[J].Journal of Nanjing Normal University(Engineering and Technology),2014,14(01):076-81.
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动力系统双曲对称的高效生成方法
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南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
14卷
期数:
2014年01期
页码:
076-81
栏目:
出版日期:
2014-03-31

文章信息/Info

Title:
Efficiently Generating Hyperbolic Symmetries of Dynamic Systems
作者:
陈 露
南京师范大学教育科学学院,江苏 南京 210097
Author(s):
Chen Lu
School of Educational Sciences,Nanjing Normal University,Nanjing 210097,China
关键词:
双曲几何; 动力系统; 同变性映射; 颜色方案
Keywords:
hyperbolic patterns; dynamical systems; equivariant mappings; color scheme
分类号:
TP391
文献标志码:
A
摘要:
对对称模型分形图形自动生成方法的探索一直是动力系统研究的一个重要分支.本文提出了一种利用动力系统方法自动生成丰富的双曲图案的算法.通过构造动力系统群下具有同变性属性的映射方程,将单位圆内的点变换到基本域内,通过动力系统群的映射,由基础域上的图形及其变换,就可得到覆盖整个区域且仅在边界处重叠的图像.根据连续两点间的双曲距离给点附颜色,这种颜色方案不仅反映了通过特定数目迭代后各个轨迹点的收敛速率,而且由于动力系统群的同变性属性,对称点拥有相同的颜色,所以生成的图像具有对称性,增强了生成图案的艺术感染力.使用该方法可以生成一系列双曲模型图案.
Abstract:
Exploration on automatic generation of symmetric patterns of fractals has been an important branch in the study of dynamical systems.In this paper,a new and fast algorithm is presented for automatically generating hyperbolic patterns using dynamical systems method.By employing the construction of equivariant mappings under the dynamical system groups,the method maps points in the unit circle to a fundamental region.We can get the entire space without overlapping except at the boundaries with the fundamental region and its transformed copies.Colors of the points is decided based on the hyperbolic distance between two consecutive points on the same orbit.It not only reflects the convergence rate of after a specific number of iterations,but also makes the symmetrical points having the same color and causing the picture to symmetry,thus enhancing the artistic appeal of the generated image.The method can generate a series of hyperbolic model patterns.

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备注/Memo

备注/Memo:
收稿日期:2013-10-22.
通讯联系人:陈露,硕士研究生,研究方向:数字几何处理.E-mail:xuriyingmei@163.com
更新日期/Last Update: 2014-03-31