具有平面晶体对称性混沌吸引子的分形极限图  

Fractal Limit Images of Chaotic Attractors with Crystallographic Symmetries

作　　者：邹玉茹[1] 鲁坚[1] 

机构地区：[1]深圳大学数学与计算科学学院,广东深圳518060

出　　处：《计算机与现代化》2009年第4期27-29,共3页Computer and Modernization

基　　金：国家自然科学基金资助项目(60873168);广东省自然科学基金资助项目(2008257);深圳大学科研启动资助项目(200850;200864)

摘　　要：提出用混沌函数构造具有平面晶体群对称性混沌吸引子的上半平面、方极限和圆极限分形图的简便方法。通过确定单个混沌吸引子所在的基本区域,利用同胚仿射变换,把基本区域中的混沌吸引子自相似地映射到上半平面,进而生成方极限、圆极限分形图。这些图案具有很好的艺术渲染力。该方法使单个混沌吸引子保持几何结构不变,但图形在整体上却具有很好分形自相似的性质。In this paper, fractal limit images of chaotic attractors with planar crystallographic symmetries are constructed by chaotic functions. These images are called half upper planar, squre limit and circle limit images. So a simple method is present here. The fundamental region of single attractor is decided and self-similarly mapped into the upper half plane by using the homeomorphic affine transformation. Then the fractal limit images of square limit and circle limit are obtained. Owing to this method, the geometric construction of the single chaotic attractor is not changed, while the whole images have well fractal self-similar properties.

关 键 词：混沌吸引子 分形自相似 极限图 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]