变周期窗口平面动力系统的构造与可视化  

Construction and Visualization of Planar Dynamic Systems with Non-equidistant Cyclic Windows

作　　者：陈宁[1] 孙艳玲[1] 孙晶[1] 

机构地区：[1]沈阳建筑大学信息与控制工程学院,沈阳110168

出　　处：《计算机辅助设计与图形学学报》2010年第5期784-790,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：辽宁省自然科学基金(20082007);沈阳市人才基金(2008140403010)

摘　　要：为了用同一个迭代映射构造出多个不同视觉效果的平面连续排列图案,提出一种用变周期窗口的动力系统生成具有P1对称特性的平面排列图案的有效算法.该算法采用余弦函数及含参的非线性角度变量构造一族使动力平面上各周期窗口的尺度变化的迭代映射;通过计算任意周期窗口和最大周期窗口得出窗口间相应点之间的非线性对应关系,并构造出各周期窗口中的混沌吸引子和充满Julia集,其图案是连续的且结构不同的;选用不同的周期窗口作为基本计算区域,使之与正方形像素矩阵对应,并构造出基本图元,实现了用一个映射构造出多个平面排列图案的算法.实验结果表明,采用文中算法可以生成大量具有P1对称的平面等距排列的混沌吸引子和充满Julia集图案.To generate planar tiling images with different visual effect by the same iterating mapping,we present a method that allows the P1 planar tessellations to be constructed by a planar dynamic systems with non-equidistant cyclic windows.We construct a family of iterative mappings,which yield cyclic windows of variant size in the dynamical plane by incorporating cosine functions and non-linear angle variables with parameters.Chaotic attractors and filled-in Julia sets in the different cyclic windows are created by establishing the coordinates of any cyclic windows and the maximal window,then clarifying the relationship of corresponding points between these cyclic windows.The respective images in different windows are continuous but with individual structures.We can choose any cyclic window as the basic computing region and stretch or compress it into a square,which is transferred to the plane to compose the planar tilling.Experimental results show the effectiveness of the proposed approach.

关 键 词：动力系统 变周期窗口 混沌吸引子 充满JULIA集 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]