中文摘要：

探讨了从动力系统角度生成具有循环群、二面体群对称性图像的不变函数方法。构造关于平面循环群、二面体群的不变函数作为密度函数,把具有循环群、二面体群对称性混沌函数作为迭代函数系统,生成具有很强艺术效果的循环群、二面体群对称性图像。同时给出了构造群对称性不变函数的理论依据。该方法为平面设计对称图像提供了一种新方法。

英文摘要：

The invariant function method for generating images with cyclic or dihedral symmetry by means of dynamical systems is investigated. By constructing the invariant functions with respect to cyclic or dihedral group which are used as density functions, and taking chaotic functions with cyclic or dihedral symmetry to be iterating functions, visually fascinating patterns with such symmetries is generated. Meanwhile, the mathematical principles of the construction of invariant function with group symmetries are given. The method presented here provides a novel approach for devising planar symmetric patterns.