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Math Help - fractal dimension of "filled" koch snowflake

  1. #1
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    fractal dimension of "filled" koch snowflake

    The box counting dimension and Hausdorff dimension of Koch snowflake(shown below left) itself is log 4/log 3 ≈ 1.26.

    I have a question: What about Koch snowflake with inside of it completely filled(shown below right)? Is the dimension 2? Or is it still log 4/log 3 ? Or something else?

    I tried computational algorithm(box counting algorithm) to calculate the dimension numerically, and it gave dimension around ~1.83. I wonder where this number come from. Is it just a numerical error of the algorithm(where the answer should be 2)?

    Thank you in advance for those reading this post.

    fractal dimension of "filled" koch snowflake-koch.giffractal dimension of "filled" koch snowflake-koch2.gif
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  2. #2
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    This might be your answer [talks about "box (fractal) dimension"].

    http://www.ncssm.edu/courses/math/TC...c_AllInOne.pdf
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  3. #3
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    Wiki perspective

    In most cases, there's no consistent definition for fractal dimension:

    Fractal dimension - Wikipedia, the free encyclopedia
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