| The calculation and estimation of the Hausdorff measure and dimension of the fractal sets is one of the important subjects of fractal geometry. The self-similar set is the most classical and in-depth studying of the fractal sets, especially the s-set, its Hausdorff dimension equals to the self-similar dimension, while there are not many re-sults about calculation of its Hausdorff measure. Based on the optimal coverage theory of the Hausdorff measure calculation, the paper researches the Hausdorff dimension and measure of some self-similar sets, such as Sierpinski gasket and Sierpinski carpet. The specific work consists as follows:In part two, we introduce the definitions and properties of Hausdorff dimension and measure. After that, we mention some skills of the computation about Hausdorff dimension and measure, such as quality distribution principle.In part three, we elaborate the generation of the self-similar fractal sets. Then for the self-similar set satisfying the open set condition, the computational theorys of Hausdorff dimension and measure are given.In part four, after constructing a suitable serial of coverage sets, we get the formu-las for calculating the upper bounds of the Hausdorff measures of Sierpinski gasket S, Sierpinski carpet C x C, a class of Sierpinski gaskets Sλ(1/3<λ≤1/2) and a class of Sierpinski carpets Cλ(1/4<λ≤1/3). With the aid of computer, the upper bounds of the S and C x C are imporved to be 0.817918996…and 1.5018469…. In addi-tion, by using the optimal coverage theory of the Hausdorff measure calculation, the accurate value Hausdorff measures of a class of Sierpinski gaskets Sλ(0<λ≤1/3) and a class of Sierpinski carpets Cλ(0<λ≤1/4) are obtained,which is 1 and(21/2)s respectively.The main results in this paper are essentially different from the previous proof pro-cess and estimation method for the upper bound. Remarkably, we can expand the meth-ods to the calculation and study on general Sierpinski gasket and Sierpinski sponge.
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