中文摘要：

探讨从动力系统角度生成具有循环群、二面体群演化对称性图像的不变函数方法。把具有循环群、二面体群对称性演化函数作为迭代函数系统，构造相应的不变函数，生成具有很强艺术效果的循环群、二面体群演化对称性图像。该方法为平面设计对称图像提供了一种新方法。

英文摘要：

This paper investigates the invariant function method for generating images with cyclic and dihedral evolving symmetry by means of dynamical systems. By taking chaotic functions with cyclic and dihedral evolving symmetry to be iterating functions and constructing their corresponding invariant functions, visually fascinating patterns with such symmetries can be generated in this way. The method presented here provides a novel approach for devising planar symmetric patterns.