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物理“海马”、数学“海马”与生物“海马”


□ 高鸿钧 时东霞 薛增泉

  摘 要在C60- TCNQ(一种有机分子名称的缩写)和纯的TCNQ有机分子薄膜中,文章作者得到了一种形似海洋中生存的动物海马的图案结构,取名为“海马”分形结构.这种“海马”图案在旋转180度时具有近似的对称性,但是不同于简单的二维反转对称.在数学中用复变函数的多项式,通过Julia对复杂空间中函数的纯粹数学映射(即z→z2+c,其中c=-0.74543+0.1130i),也能模拟出相似的“海马”图案.对于“海马”分形,文章作者提出如下的一种形成机制,即:在薄膜形成初期过程中,中性分子或团簇中存在部分荷电粒子,由于库仑排斥作用,成核和生长过程中会形成对称性破缺,最终形成“海马”状分形.“海马”的有趣图案,加深了人们对自然与科学统一的认识,激发了人们对自然本源的探索激情.
  关键词薄膜,C60-TCNQ,TCNQ,“海马”分形
  
  “Seahorses” in Mathematical, Physical and Biological Systems 
  
  GAO Hong-|Jun1,SHI Dong-|Xia1XUE Zeng-|Quan2 
   (1 Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China)
  (2 Department of Electronics, Peking University, 100871)
  
  AbstractWe describe the formation of unique “seahorse” fractal patterns in the growth of fullerene-tetracyanoquinodimethane (C60-TCNQ) and pure TCNQ thin films. These “seahorse”patterns are S-shaped forms with “fins” on the outer edges of the curved arms, like real biological seahorses. These “seahorse” fractal patterns exhibit an approximate symmetry under rotation by 180°, but strongly break two-dimensional inversion symmetry. Similar “seahorse” patterns can also be simulated by the Julia set from a pure mathematical mapping of the function in complex space: z→z2+c, with c=-0.74543+0.1130i. A novel formation mechanism is proposed, involving the charging of part of the neutral molecules and clusters in the initial stage of film growth, and the broken symmetry arising from the Coulomb repulsive force in the nucleation and aggregation process. The similarity of physical, biological and mathematical seahorses shows the consistency of nature, which should stimulate our interest for deeper scientific explorations. ......
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