关于Sierpinski垫片的Hausdorff测度的上界估计

Upper estimate of Hausdorff measure of the Sierpinski gasket

Sierpinski垫片是经典的自相似分形集,其Hausdorff维数是log23,但其Hausdorff测度的计算仍非常困难.在构造的覆盖集中,给出计算被覆盖三角形数的算法,从而估计出相应的Hausdorff测度Hs(S)≤0.817 918 996…,此结果优于目前现有文献中的已知结果.

Sierpinski gasket was known as one of the classical self-similar fractals.Its Hausdorff dimension had been determined to be log2 3,the calculation of its accurate Hausdorff measure kept very difficult to get.By constructing coverings of Sierpinski gasket,algorithm of the number of small triangles was given.An upper bound estimate（0.817 918 996 …） of the Sierpinski gasket was obtained,which was better than the known results.