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In any case, I am trying to understand fractal dimensions. I read through wikipedia's description and I believe I kind of understand it. I understand how one gets the fraction dimension for Koch snowflake or Sierpinski triangle. However, I cannot figure out the same thing for the Gosper Island. http://www.wolframalpha.com/input/?i=Gosper+Island&a=*C.Gosper+Island-_*Formula.dflt-&f2=2&x=12&y=10&f=GosperIsland.n_2 . It seems to me that it should be N = 7 and epsilon = 1/3 where N and epsilon are discussed here http://en.wikipedia.org/wiki/Fractal_dimension. However apparently Hausdorff dimension gives log(9/7) which suggests to me that N = 9 and epsilon = 1/7, which confuses me greatly.

If someone could help better understand fractal dimensions and what I am missing here I would greatly appreciate it. Thanks in advance!