构造正六面体表面混沌吸引子的平面迭代映射

为了实现用二维迭代映射构造三维球面图形,提出用平面正方形格子上的迭代映射构造三维正六面体表面上连续排列的混沌吸引子的方法.首先提出用于构造正六面体上连续排列混沌吸引子的平面迭代映射在正方形格子上应满足的边界条件;其次用截断的傅里叶三角级数构造出满足边界条件的3个平面排列迭代映射;最后找到了2个基本绘图窗口,利用3个迭代映射在2个正方形格子边界上的对称特性完成混沌吸引子在平面上和正六面体上的连续排列图形的构造.实验结果表明,文中提出的基于正方形格子的二维平面排列迭代映射可以用于大量的自动生成三维正六面体上的连续混沌吸引子图形.

Plane Iterating Mappings to Construct Chaotic Attractors on Surface of Hexahedron

To construct the spherical patterns by the nonlinear planar iterating mappings,we present a way of constructing continuous-tiling chaotic attractors on the surface of the hexahedron in 3-space by the planar symmetry mappings based on the square lattice.The conditions on the square boundary,which the planar symmetry mappings should satisfy,to construct continuous-tiling chaotic attractors on the hexahedron were proposed.Three plane mappings were formed by the truncated Fourier series.The two plotting windows were found.Based on the boundary symmetric characteristic of the two plotting windows,the chaotic attractors in the plane or on the hexahedron can be continuously generated by the three mappings.Experiments show that the planar mappings based on the square lattice presented in this paper can be used to automatically construct a great number of the continuous-tiling chaotic attractors on the hexahedron in 3-space.