複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica

Sierpinski gasket
l is the stick length (=radius for applying gaussian blur
to this picture in Photoshop)
l=1 l=1/2 l=1/4 l=1/8
N=3 N=9 N=27 N=81
So for l=(1/2) n =2 -n we want to know how N changes with l:
N=3 n = 3 -log l /log 2 = 3 -log l /log 2
3 3 = (3 log l
3 ) -1/log 2
3
= l -1 /log 2
3 =l –log 3/log 2 = (1/l) D
D=log3/log2=1.585
because for x=a y , we have y=log a
x, and a log a x =a y =x