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I've been doing some research on the Mandelbrot Set and have discovered that it's boundary is a fractal. I was wondering if the Coastline Paradox can be applied to the boundary of the Mandelbrot Set? Surely the perimeter of the set would approach infinity depending on the size of "measuring stick" we were using to measure it? Thank You!

M.Hatton
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  • What do you mean by "I was wondering if the Coastline Paradox can be applied to the boundary of the Mandelbrot Set"? Exactly what statement are you seeking to apply? –  Nov 11 '20 at 15:55
  • Well, the fact that if we use an increasingly smaller measuring stick will the length of the perimeter approach infinity? – M.Hatton Nov 11 '20 at 16:27
  • Boundary of Mandelbrot Set has Hausdorff dimension greater than 1, so how do you even define it's length? – mihaild Nov 11 '20 at 17:29
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    Yes, you're absolutely correct. You can measure the length will smaller and smaller rulers and find that your measurements tend to $\infty$. – Mark McClure Nov 11 '20 at 18:08

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