由具有D_3对称特性的Sierpinski三角形构造球内接二十面体分形图  

Construction of the Fractal on the Surface of the Inscribed Icosahedron in the Unit Sphere from Sierpinski Triangle with D_3 Symmetry

作　　者：陈宁[1] 邓斌[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：《小型微型计算机系统》2014年第8期1882-1884,共3页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61272253)资助;沈阳市科技局基金项目(F12-277-1-08)资助

摘　　要：为了生成三维空间分形图,提出将具有平面D3对称特性的Sierpinski三角形压缩到二十面体上的方法.将二十面体上的一个平面置于平行于XOY平面的位置,选取这个面为基准面,根据球内接二十面体几何特点,构造球内接二十面体;将Sierpinski三角形映射到二十面体的基准面上;通过旋转变换将基准面上的分形图旋转变换到二十面体的其它表面上,生成三维空间分形图.研究表明,可以用具有平面D3对称特性的分形图生成二十面体分形图.In order to generate fractal image in 3D, a method was proposed, which could be used to contract the Sierpinski triangle generated by the plane IFS onto the surface of the inscribed icosahedron in the unit sphere. Let a side of the inscribed icosahedron par- allel to the plane XOY. Define the plane as the basic side. According to the geometry character the inscribed icosahedron in the unit sphere was constructed. The Sierpinski triangle was mapped on the basic side of the icosahedron. The fractal on the basic side was transformed to the other sides of the icosahedron by a series of rotation transformations and the 3D fractal was constructed. The re- search result showed that the method present in this paper can be validly used to generate the fractal on the face of the inscribed icosa- hedron by the plane fractal with the D3 symmetry.

关 键 词：迭代函数系 SIERPINSKI三角形 二十面体 旋转压缩变换 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]