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Math Help - Fractals

  1. #1
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    Fractals

    Ive got a question regarding the Sierpinski Carpet. I don't understand the intuition behind the formula N = r ^ D where N is the number of squares, r is the scale factor and D is the dimension. In other words I don't understand how by knowing N, r and D you can draw a Sierpinski Carpet.

    The other thing I don't understand is why you would take logs of both sides to find D? why cant you just find it using D = logr(N)? Is it because the only way that that would work is if we have logD(r^D)? In which case why is that impossible to do?
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  2. #2
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    Quote Originally Posted by Atomic_Sheep View Post
    Ive got a question regarding the Sierpinski Carpet. I don't understand the intuition behind the formula N = r ^ D where N is the number of squares, r is the scale factor and D is the dimension. In other words I don't understand how by knowing N, r and D you can draw a Sierpinski Carpet.

    The other thing I don't understand is why you would take logs of both sides to find D? why cant you just find it using D = logr(N)? Mr F says: You can. But that's not gonna be too handy unless your calculator has a \log_r button, is it?

    Is it because the only way that that would work is if we have logD(r^D)? In which case why is that impossible to do?
    ..
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  3. #3
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    Yer just as I thought... what about the intuition behind how they got that formula.
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