Rough Mountains
The image is the total opposite of the previous smooth surface in the sense that the height function is nowhere differentiable (well, almost!) and the terrain shows a typical fractal structure. Consequently, the mountains look much more natural and realistic.
If you are interested in a detailed treatment of fractals in general and/or fractal landscapes in particular, I recommend “Chaos and Fractals, New Frontiers of Science” written by Peitgen, Jürgens and Saupe and published by Springer. It’s always easier to build your own methods after learning the principles from a good reference.
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