Fractals and Coastlines

So I just started a book called Death by Black Hole by Neil DeGrasse Tyson and he mentioned fractals, which I had heard of before but I never looked into it. Tyson said that in 1967 Benoit B. Mandelbrot posed a question asking for the length of the British coastline. That seems simple enough. Sure, Mandelbrot couldn’t just google it but he could find a map of the coastline, measure the coastline with a piece of string, and find the length using the map’s scale. However, an issue arose. As he measured the coast on maps of increasing detail he saw that the length was increasing. That’s odd. So what was the true length? Even if one was to walk along the coast with miles worth of string going around each and every rock on the beach, it would still not be the true length because one can go to the atomic level and measure around each atom. This mental exercise evolved into a new field of mathematics based on fractional (or fractal) dimensions. Mandelbrot said that the ordinary concepts of dimension are too simple to characterize the complexity of the coastline. Fractals are ideal when describing ‘self-similar’ patterns, being mainly the same at different scales. Although the perfect fractal can only be created by a computer, they can be found in broccoli, ferns, and snowflakes.

The Paradoxicality

https://sp.yimg.com/ib/th?id=JN.7AQo6MU%2f9DEfFlFOhi0myw&pid=15.1&P=0