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

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    $\begingroup$ 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 $2$. $\endgroup$ – Ng Chung Tak May 22 at 0:44
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    $\begingroup$ "Perimeter" usually refers to the length of the boundary of a shape. $\endgroup$ – Rahul May 22 at 1:54

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