A Novel Solution for the Hausdorff Measure Computation of Sierpinski Carpet

摘要

The computation of the Hausdorff measure of fractals is the basic problem in fractal geometry. However, this is very difficult. The genetic algorithm is one of optimization algorithms to resolve complicated problems of wide scope, and has great capabilities in self-organizing, self-adaptation and self-learning. Lifeng Xi professor put forward to the thought of computing the Hausdorff measure of fractals using the genetic algorithm several years ago. In this paper, we mainly discuss the realization of the genetic algorithm on the Sierpinski carpet with compression ratio 1/4 in detail, including the encoding and decoding method, generation of the initial population, fitness computation, and genetic operators. Finally the Hausdorff measure of the Sierpinski carpet with compression ratio 1/4 is obtained. Experimental results show that the genetic algorithm is an effective and universal method of calculation of the Hausdorff measure.