Fractals on the Earth
River networks - or watersheds - form fractal canyons, built by the repeated erosion from countless rainstorms over eons.
Coastlines are another common fractal on the Earth. More details emerge the closer you examine a coastline. The whole field of fractal geometry began by asking the question “How long is the coast of Britain?” The answer is that it depends on how closely you measure it, and when you examine the coastline with a finer and finer ruler, its length approaches infinity.
Bodies of water can be fractals too, as we observe in many flat, wet places. The same shapes occur over a wide range of scales, the hallmark of a fractal.