Using the quaternion expansion of the shifting number ,we determined the fractal structure of intersection of sierpinski footcloth with their translates, and set up the fundamental properties of Box dimensions of those intersection sets.
研究Sierpinski地毯平移交集的计盒维数,发现它与平移长度有关,利用移位t的四进展开式,给出一递归集,得到Sierpinski地毯平移交集的分形结构,并建立这些交集计盒维数的基本性质。