Fractals & Chaos Assignment for 2/14

We proved the necessity of fractional dimension today and derived the formula S^d = N as a way of finding fractional dimension. For the Sierpinski triangle, for example, each time we cut the baseline in half, we triple the number of pieces at that scale. So for Sierpinski’s triangle, S = 2 and N = 3, giving us 2^d = 3. Your homework tonight is to simply solve for d, which is the dimension of Sierpinski’s triangle (to be more correct, this is the triangle’s Hausdorff Dimension).


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