通过构造扩展Picard群等变的映射,从动力系统的角度出发,利用计算机自动生成具有扩展Picard群对称的图案,生成的图案在与xy平面平行的截面上的对称性为pmm晶体群对称，在包含x轴的截面上为扩展模群对称。 从数值实验所生成的图案可以看出，该算法生成的图案具有丰富的艺术性,为铺砌、雕塑等设计提供了一种计算机自动生成的新途径。

3D tiling patterns with the symmetry of the extended Picard group are automatically generated by means of dynamic systems equivalent to the extended Picard group.The derived patterns have the symmetry of the wallpaper group pmm on the cross section plane parallel to the xy plane,and own the symmetry of the extended modular group on the cross section plane containing the x axis.The numerical experiments show that the generated patterns are artistic.The method provides a novel approach to devise exotic symmetric tiling patterns from a dynamic system’s point of view.