盒维数的不确定性与迭代分形维数的算法

The Uncertainty of Box-counting and Counting of Iterative Fractal

盒维数是分形几何中的一个重要概念,“数盒子法”广泛用于应用学科.盒维数具有不确定性,对于迭代分形对象,其迭代方法与分维数、盒维数存在直接联系,从迭代方法中构造数列,通过数列求得的盒维数,正好与分维数相等.

Box - counting is an important definition in fractal geometry, and box- counting method is widely used in applied subjects. We discover that box - counting has the characteristic of uncertainty. As for iterative fractal object, iterative method directly affeetes fractal dimension and box - counting. If we build sequence of number with iterative method and we will get box - counting with sequence of number, which is exactly equtl to fractal dimension.