# “Border” versus “perimeter” for Mandelbrot sets

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

• 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 at 0:44
• "Perimeter" usually refers to the length of the boundary of a shape. – Rahul May 22 at 1:54