平面晶体对称拼砌图像的计算机生成方法  

A Computer Generation Method for Planar Tiling Patterns with Crystallographic Symmetries

作　　者：叶瑞松[1] 邹玉茹[1] 

机构地区：[1]汕头大学数学系,广东汕头515063

出　　处：《工程图学学报》2006年第5期86-93,F0003,共9页Journal of Engineering Graphics

基　　金：数学天元基金资助项目(A0324649);广东省自然科学基金资助项目(032035)

摘　　要：利用三角函数的周期性,生成具有晶体群p1,p2,pm,pg,pmm,pmg,pgg,cm,cmm对称性的迭代函数系统,该类迭代函数系统的混沌吸引子具有系统本身的对称性。从动力系统的角度,探讨了如何利用具有晶体对称性的动力系统来生成平面对称的彩色拼砌图像。从数值实验所生成的图像可以看出,该方法能容易地生成漂亮的图像,生成的图像具有丰富的艺术性,为平面铺彻图像的设计提供了一种计算机自动生成的新途径。Making use of the periodicity property of trigonometric functions, one can derive iterated function systems with the symmetries of crystallographic groups p1, p2, pro, pg, pmm, ping, pgg, cm, cmm. The chaotic attractors of the constructed systems have the same symmetries as the systems themselves. The paper discusses how to apply the dynamical systems with crystallographic symmetries to generate colored tiling patterns from a dynamical system＇s point of view. The method presented here is easy to create exotic tiling patterns with crystallographic symmetries; it can be observed that the tiling patterns are artistic. The method provides a novel approach for devising planar symmetric tiling patterns.

关 键 词：计算机应用 平面晶体对称拼砌 迭代函数系统 群 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]