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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (8): 983-990.doi: https://doi.org/10.1007/s10483-009-0804-5

• Articles • 上一篇    下一篇

Fractal geometry and topology abstracted from hair fibers

殷雅俊1,2，杨帆1，李颖1，范钦珊2   

  1. 1. Department of Engineering Mechanics, School of Aerospace, AML, Tsinghua University,Beijing 100084, P. R. China;
    2. Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China
  • 收稿日期:2009-05-14 修回日期:2009-06-29 出版日期:2009-08-01 发布日期:2009-08-01

Fractal geometry and topology abstracted from hair fibers

YIN Ya-Jun1,2, YANG Fan1, LI Ying1, FAN Qin-Shan2   

  1. 1. Department of Engineering Mechanics, School of Aerospace, AML, Tsinghua University,Beijing 100084, P. R. China;
    2. Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China
  • Received:2009-05-14 Revised:2009-06-29 Online:2009-08-01 Published:2009-08-01

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摘要： Based on the concepts of fractal super fibers, the (3, 9+2)-circle and (9+2,3)-circle binary fractal sets are abstracted form 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 concerned, the following propositions are proved: The (9+2) topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent (or fundamental). Besides, we demonstrate that the (3, 9+2)-circle and (9+2, 3)-circle fractal sets are golden ones with symmetry breaking.

关键词: hair fibers, (9+2) topological patterns, symmetry breaking, binary fractal sets, fractal geometry

Abstract: Based on the concepts of fractal super fibers, the (3, 9+2)-circle and (9+2,3)-circle binary fractal sets are abstracted form 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 concerned, the following propositions are proved: The (9+2) topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent (or fundamental). Besides, we demonstrate that the (3, 9+2)-circle and (9+2, 3)-circle fractal sets are golden ones with symmetry breaking.

Key words: hair fibers, (9+2) topological patterns, symmetry breaking, binary fractal sets, fractal geometry

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