整自相似集Hausdorff测度上界的变化因素分析

The Analysis of changing Factors of the Upper Bound of Hausdorff Measure for Self-similar Fractal Sets

分形集Hausdorff测度的估计是分形理论中的一个基本问题。文献[1]得到了整自相似集Hausdorff测度上界估计的公式,在此进一步分析影响整自相似集的Hausdorff测度上界的因素,探讨通过计算方法的选取对所给的整自相似集Hausdorff测度上界给出一定的影响。

It is a basic question in fractal geometry to estimate the Hausdorff measure of fraetals. We obtain a formula to estimate the upper bound of Hansdorff measure for integral self-similar fractal sets and further analyzes the changing factors of on the upper bound of Hausdorff measure. We find that different computational method has impact on the upper bound of Hausdorff measure.