Fractals are an important tool for procedural generation.

A fractal is a pattern that has a repeating pattern over multiple scales. Since they create amplification–complex patterns from simple inputs–they can be an effective way to add detail. Additionally, since many natural things exhibit self-similar fractal patterns–mountain ranges, coastlines, trees, ferns, clouds, lightning–fractals are useful for approximating them. There 

The pictures above are successive frames from a deep zoom into the Mandelbrot set. As you zoom deeper, you can see that the larger structures are repeated at smaller and smaller scales, in different configurations, neverending. Zoom deep enough in the right place and you’ll find distorted versions of the whole Mandelbrot set that themselves contain distorted versions of the entire set.

One of the critical things that enabled Benoit Mandelbrot to explore fractals in depth was the then-new computer-visualisation of fractals, which allowed the previously abstract mathematical functions to be seen rather than just imagined or roughly approximated. Some of the earliest terrain generation came from these computer visualization experiments with fractals.