Sierpinski垫片的Hausdorff测度上估算法的Java实现

Implementation of the Upper Extimation Algorithm of the Hausdorff Measure of Sierpinski Gasket with Java

测度与维数的估计和计算对于分形而言,既是十分重要,也是十分困难。作为三大经典自相似集之一的Sierpinski垫片,尽管维数容易,但测度的计算仍是非常困难。Sierpinski垫片的Hausdorff测度的计算结果更难且少。经过部分学者的研究,对Sierpinski垫片的Hausdorff测度通过不同的计算方法,均未达到理想的准确值,但得到比较接近的上界估算值。引用文献[1]的Sierpinski垫片的Hausdorff测度上估算法,用Java实现窗口对话,并计算出其算法的结果,同时存于Excel文档中。

It is very important and difficult for the measure and the calculation of measure and dimension of the fractal. As one of the three classical self similar sets, Sierpinski Gasket is difficult to measure, although it is easy to dimension. The calculation of the Hausdorff measure of Sierpinski gasket is more difficult and less. The Hausdorff measure of the Sierpinski gasket by different calculation methods does not reach the accurate value of the ideal, but being relatively close to the upper bound estimates. Refers to the Hausdorff measure of the the Sierpinski gasket estimation method, which is in the paper [1]. Uses Java to achieve dialog window, it calculates the results of the algorithm,and to remain in the Excel document.