构造球面对称充满Julia集  

Construction of Symmetrical Filled-in Julia Sets on Spherical Surfaces

作　　者：陈宁[1] 林秋芳[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：《计算机研究与发展》2013年第2期394-400,共7页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(61272253);辽宁省教育厅基金项目(L2010448);沈阳市科技局基金项目(F12-277-1-08)

摘　　要：为连续构造球面上具有多吸引周期轨道的充满Julia集图形,提出了一个关于构造任意投影面的半球面图形的算法.首先自动挑选可使动力系统迭代轨道的平均离散速度指标值L<0的参数;其次,用建立在以球心为原点的坐标系下的迭代映射,通过坐标变换,跟踪与任意坐标系相应的投影面的上半球面上各点的迭代轨道,搜索出半球面上所有互不相同的吸引周期轨道,并建立轨道链表;进一步计算投影面的上半球面各点的迭代轨道到达吸引周期轨道所需要的迭代次数,根据迭代次数为球面上的相应点指定颜色并构造出半球面上的对称充满Julia集图形.研究结果表明,采用该算法可以大量生成对称的球面充满Julia集图形.To continuously generate the images of filled-in Julia sets with attracting orbits of multi- periodicity on a spherical surface, a method of constructing a half spherical surface image on a discretional projective plane is presented. Firstly, the parameters are automatically selected to construct a spherical surface dynamic system whose Lyapunov exponent （L） is less than 0. Then, the iterating orbits of the points on the upper half spherical surface on a discretional projective plane are tracked with the mapping founded in the coordinates system whose origin is the spherical center by the coordinates transform. All the different attracting orbits are built in a link list. Finally, every point on the spherical surface is pointed a color according to the iterating number by which its iterating orbit goes to an attracting orbit in the list, and the filled-in Julia set image on the upper half spherical surface is constructed. The result shows that the method can be used to generate a great number of symmetric filled-in Julia set images on the sphere surface.

关 键 词：球面 对称 动力系统 LYAPUNOV指数 充满JULIA集 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]