Multiple-cell elements and regular multifractals  

作　　者：殷雅俊 李颖 杨帆 范钦珊 

机构地区：[1]Department of Engineering Mechanics,School of Aerospace,AML,Tsinghua University [2]Division of Mechanics,Nanjing University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第1期55-65,共11页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10872114);the Natural Science Foundation of Jiangsu Province (No. BK2008370)

摘　　要：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 con- struction 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.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 con- struction 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.

关 键 词：binary fractal fibers binary cell elements regular binary fractals multiplecell elements regular multifractals 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]