一种■_BF<■_BF分形集的构造

A Construction of Fractal Sets Satisfying ■_BF<■_BF

在所有介绍盒维数的分形文献中,仅仅都是在理论上指出存在满足dimBF<dimBF的分形集,都没有给出具体的例子,原因是这种集很复杂不易验证和说明.文章利用三分康托集的一个变化,构造出一种较简单且易验证和说明的满足dimBF<dimBF的分形集.

All of the bibliography of introducing fractals only point out that there are fractral sets satisfying dim↓-BF〈↑dimBF, Because the sets not easy to proof and explanation, so all of them don＇ t quote concrete examples. In my paper, a construction of fractral sets satisfying dim↓-BF〈↑dimBFand easy to proof and explanation are given by using a change of 3-part cantor set.