不变映射生成三维对称镶嵌图案

从动力系统的角度出发,通过构造群P6和P4不变的映射,利用计算机自动生成具有P6和P4对称的图案,生成的图案在与xy平面平行的截面上对称性分别为p6m和p4m晶体群对称.改进了传统的采用等变映射生成三维镶嵌图案的繁杂方法,用计算机自动生成了漂亮的三维镶嵌图案,为铺砌、雕塑等设计提供了一种新途径.

Three-Dimensional Tiling Patterns Generated by Invariant Maps

Three-dimensional tiling patterns with the symmetries of the groups P6 and p4 are generated by constructing invariant maps from the dynamical system＇s point of view. The derived patterns own the symmetries of the wallpaper groups p6m and p4m on the cross section planes parallel to the xy-plane respectively. The proposed method improves the complexity in constructing the equivariant maps to generate three-dimensional tiling patterns. The method provides a simple approach for devising exotic symmetric tiling patterns in three-dimensional space.