一类Sierpinsk i地毯的分细分析方法和其Hausdorff测度准确值

Subdivisional analytical method of a kind of sierpinski carpet and the exact hausdorff measure value

计算一类Sierpinski地毯的Hausdorff测度,利用投影降低分形维数及分形的分细分析方法,得到了这一类Sierpinski地毯的Hausdorff测度准确值.当这类Sierpinski地毯的Hausdorff维数s∈[log54,1]时,有Hausdorff测度准确值为Hs(S)=1.

By using fractal subdivisional analytical method and projecting to lessen fractal dimension,a kind of Sierpinski carpet exact Hausdorff measure value is obtained. Concretely, when the kind of Sierpinski carpet Hausdorff dimension satisfies s∈[log_54,1], the kind of Sierpinski carpet excat Hausdorff measure value is H^s(S)=1.