A coastline's length changes depending on the size of ruler you measure it with

Measure Britain's coast in 100km segments and you get about 2,800km; switch to 50km segments and it jumps to roughly 3,400km, because finer rulers catch more inlets and bends. Mathematician Benoit Mandelbrot used this 'coastline paradox', first noted by Lewis Fry Richardson, to help found fractal geometry. In principle, an infinitely fine ruler makes a coastline's length infinite.

— Benoit Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension — Science, vol. 156, no. 3775, 1967