超级分形管分形维数的上限与下限

超级分形管在结构和几何上都具有很强的自相似性,因此,通过选择一个特殊的覆盖单元——一个管就可以基于数格子法计算它的分形维数,推导出基于各级的拓扑结构分别为Zigzag和armchair的超级分形管的分形维数公式。虽然只有有限级的超级分形管在工程是可用的,但其结果为设计新型的超级分形天线、超级分形格栅以及分形电路中的电子器件提供了思路和启发。

Upper and Lower Bounds of Fractal Dimensions for Fractal Super Tubes

Fractal super tubes with strict self-similarities both in structure and in geometry make the box-counting method feasible and efficient in calculating their fractal dimensions only by choosing a special covering set -- a common tube. The fractal dimensions of fractal super tubes with zigzag topology and armchair topology are formulated at all scales respectively. Although fractal super tubes with limited levels could be applied in engineering structures, the results of this paper will provide new enlightenment on the design of fractal super antennas,fractal super lattices and electronic apparatus in fractal circuits.