The Hausdorff Measures Of Two Kinds Of Fractal Sets On Plane

This paper discusses the problem on calculation of the Hausdorff measures of two kinds of fractal sets on Plane.Firstly, the Hausdorff measure of Sierpinski Carpets with various similar ratio is studied systemically: when similar ratio α = 1/2 ,we obtain an advanced estimation of upper boundary of the Hausdorff measure through constructing special s -cover and using the homogeneous property the Hausdorff measure, and a better value of its lower boundary is get via "Method of Plotting Diameter"; when α ∈ (1/3,1 / 2) ,basing attractor theory of IFS, we have the continuity of Hausdorff measure map; when α ∈ (0,1 / 3], the accurate value of Hausdorff measure is found using fractal projection and the structure of Cantor Set.Secondly, we discuss a especial fractal, named "Square Flower", in Reference [1]. Through setting up an estimating formula, an upper boundary of its Hausdorff measure is gained; at the same time, we also estimate effectually its lower boundary using "Method of Plotting Diameter" mentioned above and the Theory of Quality Distributing.