摘要
研究经典分形集Sierpinski三角垫的Hausdorff测度的上界估计,构造了Sierpinski三角垫的某种覆盖六边形,给出了这个覆盖集中小三角形的个数以及覆盖的直径的计算公式,据此获得了Sierpinski三角垫的Hausdorff测度的一个更好的上界估计值Hs(S)≤(137 781÷109 286_×2 431÷3 072s≈0.870 031 853。
Abstract： The central task on the investigation of the fractal sets is to calculate or estimate Haus- dorff dimension and Hausdorff measure. In this paper, the upper bound estimation on Hausdorff mea- sure of Sierpinski gasket is investigated. The laws about the number of small triangles which are sum- marized in the coverage and the diameter of the coverage are summed up by the part-estimation method.Using these laws, a better upper bound estimation value Hs（S）≤137781/109286×（2431/3072）s≈0.870 031 853 on the Sierpinski gasket is obtained.
出处
《咸阳师范学院学报》
2011年第6期12-14,共3页
Journal of Xianyang Normal University
