【摘要】 分形集Hausdorff测度的估计是分形理论中的一个基本问题。对于一般的分形集而言,它们的Hausdorff测度准确值的计算,甚至是上下界的估计都是很困难的。即使对于一些经典的分形集也是这样。论文利用遗传算法计算出了压缩比为1/2的Sierpinski垫片Hausdorff测度的上界值,并针对计算过程中的编码方法、解码方法、群体的初始化以及适应度计算等一系列问题进行了详细分析,同时也为其他分形集Hausdorff测度的计算提供了一个通用、有效的方法。更多还原

【Abstract】 It is a basic question in fractal geometry to estimate the Hausdorff measure of fractals.However,this is very difficult even for the classicial fractals.In this paper,the upper bounds of the Hausdorff measure of Sierpinski gasket with compression ratio 1/2 was obtained by using the genetic algorithm.The realization of the genetic algorithm was discussed in detail,and at the same time it was proved that the Genetic algorithm is an effective method to calculate the Hausdorff measure of fractals.更多还原