Semi related: There's a cool rabbit hole you can dive into when it comes to coastline lengths of some countries. Specifically the UK.
Depending on who measured the coastline and with which method the results can be wildly different because there's always some form of simplification required. See this video for example: Link
I actually met Benoit Mandelbrot when I was an intern at IBM's T. J. Watson research center in the late '80s. I was randomly walking around the building and passed by a tiny office with "B. Mandelbrot" on the door. I stuck my head in, saw an old bald dude sitting there and said "are you the Bernard Mandelbrot?" He said "yes" and I said "oh" and walked on. Apparently he didn't hear that I said "Bernard" instead of "Benoit".
From the mandelbrot boundary wiki: "Images of the Mandelbrot set exhibit an infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications"
