一种计算自相似tile边界维数的方法

A Method for Computing the Hausdorff Dimension of the Boundary of a Self-affine Tile

在Hausdorff度量下,引入接触矩阵C,找到一种有效的方法来计算自相似tile边界的Hausdorff维数。T(A,D)是一个自相似tile,在n维Euclidean空间中,有公式:dimH(T)=logλ/logc。其中λ为接触矩阵的特征值,c为扩充因子。并将这个公式进一步的改进推广,使之也能够计算(A,D)为本原的且不满足等价条件时的情况。

The contact matrix C is introduced, and an effective method is given for computing the Hausdorff dimension of the boundaries of the self-similar tile in n-dimension Euclidean space： dimH （（偏低）T） =logλ/logc. Where 2 is the largest eigenvalue of the contact matrix, c is expansive factor. Beside that, we extend this method to suit for （A, D） is primitive and not satisfied the equivalent conditions.