多重胞元和规则多重分形

殷雅俊; 李颖; 杨帆; 范钦珊

doi:10.3879/j.issn.1000-0887.2010.01.006

多重胞元和规则多重分形

doi: 10.3879/j.issn.1000-0887.2010.01.006

1.
清华大学航天航空学院工程力学系,北京 100084;2.南京工业大学力学部,南京 211816

基金项目: 国家自然科学基金资助项目(10872114);江苏省自然科学基金资助项目(BK2008370)

详细信息

作者简介:
殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:yiny@jtsinghua.edu.cn).

中图分类号: Q811.6;O184
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- 被引次数: 0
出版历程
- 收稿日期: 2009-07-09
- 修回日期: 2009-11-10
- 刊出日期: 2010-01-15

Multiple Cell Elements and Regular Multifractals

1.
Department of Engineering Mechanics, School of Aerospace, AML, Tsinghua University, Beijing 100084, P. R. China;

摘要

摘要: 以超级分形纤维和双重分形纤维的研究结果为基础，达成了如下目标：首先，归纳、抽象出了多重胞元概念；其次，基于多重胞元概念，证实：具有严格自相似性的规则多重分形，不仅是可构造的，而且其构造模式具有普遍性；再者，通过分析构造模式，发现：任何规则多重分形，都可以在多重胞元意义下，被精确地等价成具有多重精细结构的广义单重分形．而基于这种等价性，单重分形维数公式就能够推广至规则多重分形维数公式，单重分形几何就能够推广至规则多重分形几何；最后，借助规则多重分形，构造了几种黄金分形．
- 双重分形纤维 /
- 双重胞元 /
- 规则双重分形 /
- 多重胞元 /
- 规则多重分形
Abstract: Based on fractal super fibers and binary fractal fibers, the following objectives were approached: Firstly, the concept of multiple celle lements was induced and abstracted. Secondly, th rough multiple cell elements, regular multifractals with strict self-similarities were confirmed not only constructible, but also being of universal construction mode. Thirdly, through the construction mode, a regular multifractal was found to be equivalent to a generalized regular single fractal with multiple fine structures under the meaning of multiple cellelements. On the basis of this equivalence, the dimension of single fractals was extended to that of regular multifractals, and the geometry of single fractals was extended to that of regular multifractals. Fourthly, through regular multifractals a few golden fractals were constructed.
- binary fractal fibers /
- binary cell elements /
- regular binary fractals /
- multiple cellelements /
- multifractals

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参考文献(20)

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