从毛发纤维中抽象出的分形几何与拓扑

Fractal Geometry and Topology Abstracted From Hair Fibers

以羊毛纤维和人类头发为原型,以超级分形纤维概念为基础,抽象出了(3)分圆和(9+2)分圆分形集,构造了(3,9+2)分圆和(9+2,3)分圆双重分形集.针对(9+2)拓扑花样,证明了这样的命题:(9+2)拓扑花样精确地存在,但不唯一,其总个数为9,其中有2种同素异构体,即9种拓扑花样中,只有2种是独立(或基本)的.另外证实了(3,9+2)或(9+2,3)分圆分形花样是一个对称性破缺的黄金分形.

Based on the concepts of fractal super fibers, the （3,9 ＋ 2）-circle and （9 ＋ 2,3）-circle bi- nary fractal sets were abstracted from such prototypes as wool fibers and human hairs, with the （3）- circle and the （9 ＋ 2）-circle fractal sets as subsets. As far as the （9 ＋ 2） topological patterns are concemed, the following propositions were proved： The （9 ＋ 2） topological patterns acogat^ly exist, but theyare of no uniqueness. Their total number is 9. Among them there are only 2 allotropes. In anoth- er word, among the 9 topological patterns only 2 are independent （or fundamental）. Besides, it was demonstrated that the （3,9 ＋ 2 ） -circle and （9 ＋ 2,3 ） -circle fractal sets are golden ones with symmetry breaking.