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Why do most writers used "border"--not "perimeter"--for Mandelbrot sets?

David G. Stork
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Daruis soli
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    The $M$-Set doesn't have finite measurement of perimeter due to its fractal nature. We usually use the term exterior boundary; in fact, the "border" has hausdorff dimension of $2$. – Ng Chung Tak May 22 '19 at 00:44
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    "Perimeter" usually refers to the length of the boundary of a shape. –  May 22 '19 at 01:54

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