动力系统生成晶体群圆极限分形图  

FRACTAL CIRCLE LIMIT IMAGES OF CRYSTALLOGRAPHIC GROUPS GENERATED FROM DYNAMICAL SYSTEMS

作　　者：鲁坚[1] 邹玉茹[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：《计算机应用与软件》2009年第8期18-19,55,共3页Computer Applications and Software

基　　金：国家自然科学基金项目(60873168);广东省自然科学基金(2008257)

摘　　要：提出从动力系统角度出发构造具有自相似性质的平面晶体群圆极限分形图的有效方法。根据Carter晶体群迭代函数系统周期性确定2π为基本区域,利用同胚仿射变换,建立基本区域到上半平面的自相似映射关系,进而通过保角映射生成圆极限分形图。同时,对Carter混沌函数进一步探讨了边界着色平滑构图条件,并生成了相应的圆极限分形图。这些图案具有很强的艺术渲染力。该方法为平面设计对称图像提供了一种新途径。An effective algorithm is presented for forming fractal circle limit planar patterns with self-similar properties in term of dynamical systems. The size of the fundamental region is defined as 2π according to the periodicity of iterating function system of ＂Carter＂ crystallographic groups. The self-similar mapping relationship is built from fundamental region to upper half plane by using homeomorphic affine transformation, and then the fractal circle limit patterns are generated by conformal mapping. Meanwhile, as for ＂Carter＂ chaotic functions, we further discuss the condition of composing smooth image by colouring the boundary points, and corresponding fractal circle limit patterns are crea- ted in this way. These patterns have so strong artistic rendering effect, the method proposed here provides a novel approach for the graphic design of symmetric images.

关 键 词：混沌 晶体群 分形 “Escher”极限图 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O175.1[自动化与计算机技术—计算机科学与技术]