多重胞元和规则多重分形

Multiple Cell Elements and Regular Multifractals

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.

Based on fractal super fibers and binary fractal fibers, the following objectives were approached： Firstly, the concept of multiple cell elements was induced and abstracted. Secondly, through multiple cell elements, regular multifractals with strict serf-similarities were confirmed not only constructible, but also being of universal construction mode. Thirdly, through the construction mode, a regular multifractat was found to be equivalent to a generalized regular single fractal with multiple fine structures under the meaning of multiple cell ele- ments. 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.