双曲对称中的分形集

Fractal Sets in Hyperbolic Symmetry

目的将分形集通过双曲变换压缩入双曲极限圆中,构造具有分形特性的极限圆图案.方法分析双曲对称群的特点,改造欧式平面上构造经典分形的IFS迭代函数系,利用这种迭代函数系与双曲平面对称变换构造出组合IFS,通过随机挑选组合IFS中的仿射变换,构造双曲排列的分形集.结果实现了将欧式平面的经典分形集以及普通的汉字压缩到了双曲平面上.结论笔者所提出的构造技术可以用于生成包含经典分形的双曲对称图案以及双曲对称排列的汉字艺术图案.

To construct the patterns with hyperbolic symmetry which are composed of classical fractals,we compress the fractal sets into the hyperbolic limit disc by the hyperbolic symmetry transformations.We recall the characteristics of the groups with hyperbolic symmetry and improve the IFS iterated function systems which are used to construct the classical fractal sets in the Euclidian plane.We obtain the combinatorial IFS iterated function systems with the iterated function systems improved and symmetry transformations in hyperbolic plane.The hyperbolic symmetry images including the classical fractals are constructed by randomly choosing the affine transformation from the combinatorial IFS.Furthermore,the hyperbolic symmetry images including the Chinese characters are also constructed.The technique presented in this paper can be used to generate both types of hyperbolic symmetry patterns with classical fractals and Chinese words.