Drawing the USA with an increasing number of edges
Reminds me of this interesting phenomenon:
One important thing to note, because I see this a lot: this doesn't mean coastlines are literally infinite in length; it's a demonstration of how our current measurement system is flawed when it comes to coastlines. Coastlines can be measured in a way that'd make them finite, however the system works well enough that (it sounds like) no one has bothered to come up with a better, widely adopted alternative.
Also, I think I've read this can be applied to borders in general? That they use the same system for measuring the borders between countries, states, cities, etc. so any border could become infinite if the precision gets high enough.
Just fractal things. No matter how far you zoom in, it's not going to be a smooth continuous function