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Applied Mathematics and Mechanics

, Volume 31, Issue 1, pp 55–65 | Cite as

Multiple-cell elements and regular multifractals

  • Ya-jun Yin (殷雅俊)Email author
  • Ying Li (李颖)
  • Fan Yang (杨帆)
  • Qin-shan Fan (范钦珊)
Article

Abstract

Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper: First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the construction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.

Key words

binary fractal fibers binary cell elements regular binary fractals multiple-cell elements regular multifractals 

Chinese Librarary Classification

Q811.6 O184 

2000 Mathematics Subject Classification

28A80 74L15 92C10 

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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Ya-jun Yin (殷雅俊)
    • 1
    • 2
    Email author
  • Ying Li (李颖)
    • 1
  • Fan Yang (杨帆)
    • 1
  • Qin-shan Fan (范钦珊)
    • 2
  1. 1.Department of Engineering Mechanics, School of Aerospace, AMLTsinghua UniversityBeijingP. R. China
  2. 2.Division of MechanicsNanjing University of TechnologyNanjingP. R. China

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