Help understanding Hausdorff dimension of Sierpinski triangle

Discussion in 'General Math' started by Johan Lans, Apr 22, 2007.

  1. Johan Lans

    Johan Lans Guest

    I'm trying to understand this with fractal dimensions, and thought I
    got it until I wanted to calculate the dimension of the Sierpinski
    triangle.
    The formula i use is d=log(N)/log(P/p) , where d is dimesion, N is
    the number of units that fit into the larger object, P is the size of
    the entire object, and p is the size of the smaller units.
    Consider Sierpinski triangle made out of three smaller triangles, the
    middle triangle is missing.
    The size of P is 1 (one big triangle). The size of a small triangle
    is 1/4 of the big one. N is three small triangles that fit into the
    bigger one. This gives me d=log(3)/log(4), which is not the correct
    answer. Where do i go wrong?

    /Johan
     
    Johan Lans, Apr 22, 2007
    #1
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  2. "Size" here should refer to diameter, not area. The size of a
    small triangle is 1/2 the size of the big one.
     
    Robert Israel, Apr 22, 2007
    #2
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  3. Johan Lans

    Johan Lans Guest

    Robert Israel skrev:
    Alright. thanks a lot. Is it the same way when dealing with three
    dimensional objects?

    /Johan
     
    Johan Lans, Apr 22, 2007
    #3
  4. Johan Lans

    israel Guest

    It's the same in any metric space.

    Robert Israel
    Department of Mathematics http://www.math.ubc.ca/~israel
    University of British Columbia Vancouver, BC, Canada
     
    israel, Apr 22, 2007
    #4
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