一类含参变量的Sierpinski垫片的Hausdorff测度

The Hausdorff Measure of a Class of Sierpinski Carpets with Parameter

Sierpinski垫片是具有严格自相似性的经典分形集之一.本文给出了一类含参变量的Sierpinski垫片.通过它在x轴上的投影估计了这类Sierpinski垫片的Hausdorff测度的下界,然后精心构造了一个仿射变换,将参变量的范围由(0,π/3)的讨论转换到(π/3,π)的讨论,从而得到了这类Sierpinski垫片的Hausdorff测度的精确值.

Sierpinski carpet is one of the classic fractals with strict self-similar property. In this paper, we will give a class of Sierpinski carpets with parameter. The lower bound for the Hausdorff measure of this kind Sierpinski carpet with parameter is given by the project on x-axis, At the same time, through a skillful affine mapping that was constructed, we transfer the parameter which in the interval （0,π/3） into the interval （π/3,π） . Finally the exact value of the Hausdorff measure of these sets is obtained.