基于数学规则的龟背纹自动生成方法

龟背纹是一种中国民间装饰纹样，一般为六角形连续状几何纹样。通过分析龟背纹的构图规则，提出了一种传统民间纹样生成算法。首先分析了龟背纹的最基本组成元素——图元，根据不同图元的对称性获得了组成图元的基本要素；然后通过旋转基本要素获得图元，平铺图元后获得整个龟背纹图案。通过定义符号，将图元生成流程参数化，获得了一般龟背纹的通用生成公式。仿真实验结果表明，通过调节生成公式参数，可生成具有不同细节的龟背纹样。

Automatic Generation Method of Turtle Back Pattern Based on Mathematical Rules

Turtle back pattern is a kind of Chinese folk decorative pattern, generally hexagonal continuous geometric pattern. By analyzing the rules of turtle back pattern composition, a new algorithm of traditional folk pattern generation is proposed. Firstly, the most basic elements of turtle ridges (called primitives) are analyzed, and the basic elements of primitives are obtained according to the symmetry of different primitives. Then by rotating the basic elements to obtain primitives, and tiling primitives to obtain the entire turtle back pattern. By defining symbols and parameterizing the generating process of primions, a general generating formula of tortoise back pattern is obtained. The simulation results show that the tortoisesback patterns with different details can be generated by adjusting the parameters of the generating formula.