一类三维Sierpinski海绵的Hausdorff维数

摘要

文章构造了一类三维Sierpinski-2n+1(n∈N)海绵，利用满足开集条件的压缩自相似映射的性质，给出它们的Hausdorff维数s=ln(n+1)3/ln(1/ε).%The paper constructs the type of generalized three dimensional Sierpinski -2n+1(n∈N) sponge and find out its Hausdorff dimension s=ln(n+1)3/ln(1/ε).by making use of the contraction of identical mapping which meets the open set conditions.