複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
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Sierpinski gasket<br />
l is the stick length (=radius for applying gaussian blur<br />
to this picture in Photoshop)<br />
l=1 l=1/2 l=1/4 l=1/8<br />
N=3 N=9 N=27 N=81<br />
So for l=(1/2) n =2 -n we want to know how N changes with l:<br />
N=3 n = 3 -log l /log 2 = 3 -log l /log 2<br />
3 3 = (3 log l<br />
3 ) -1/log 2<br />
3<br />
= l -1 /log 2<br />
3 =l –log 3/log 2 = (1/l) D<br />
D=log3/log2=1.585<br />
because for x=a y , we have y=log a<br />
x, and a log a x =a y =x