Sorry if my question is vague, as I have very little background with fractals and measure theory. My question is inspired by a tweet, where a light shone onto the mandelbrot set, and certain rays were blocked upon intersection with the set. One commenter asked what the maximum "fraction" of the total set would be "visible" to the light. That is, what proportion of the perimeter of the set would contain intersections with the light ray. I was uneasy with this question, as I was not sure if speaking of such proportions would be meaningful. For instance, I know that speaking of "fraction of natural numbers n such that n ≡ 0 (mod 3) is not strictly answerable, as there is no uniform measure on the naturals.
TL;DR: Is there a meaningful way to speak about a "fraction" of the boundary of the Mandelbrot set?
