p旋转对称IFS奇怪吸引子的[p,q]^+双曲排列

Hyperbolic Tilings with [p,q]^+ Symmetries About the Strange Attractors from IFS with p-Rotational Characteristics in Euclidean Plane

具有p旋转对称特性且含有多个压缩仿射变换的IFS迭代函数系被进一步旋转压缩到[p,q]+双曲平面的中心格子上.通过双曲几何的等变换矩阵的双曲对称排列,将普通平面上的具有旋转对称特性的有界不变集排列在双曲圆内并生成[p,q]+双曲图案.本文所提出的构造技术可以用于生成任意有界的平面对称奇怪吸引子的双曲对称排列图案.

To construct the images with hyperbolic symmetry [p,q]^＋ from Iterated Function Systems, the IFS with p-rotational symmetry characteristics , which were composed of multi-contraction affine transformations, were further compressed and rotated to the central lattice of a hyperbolic plane [p,q]^＋. The strange attractors from IFS, limited in the central lattice, were translated to the whole hyperbolic plane by the isometry transformations of hyperbolic geometry. A method was presented about how to generate images with [p,q]^＋ symmetry from the ordinary and bounded fixed sets with rotational symmetry. The method can be used to construct the hyperbolic symmetry images from any bounded symmetry strange attractors in Euclidean plane.