Fractals in nature

The mathematician Benoit Mandelbrot defined fractals simply as follows: "A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole".

Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. Fractal-like patterns occur widely in nature, in phenomena as diverse as clouds, river networks, geologic fault lines, mountains, coastlines, animal coloration, snow flakes, crystals, blood vessel branching, actin cytoskeleton, and ocean waves.