Fractal landscape

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A fractal landscape is essentially a three-dimensional form of the fractal coastline, which can be considered a stochastic generalization of the Koch curve. The Hausdorff-Besicovitch dimension, D, is a fraction between 2 and 3.

A way to make such a landscape is to employ the random midpoint displacement algorithm, in which a square is subdivided into four smaller equal squares and the center point is vertically offset by some random amount. The process is repeated on the four new squares, and so on, until the desired level of detail is reached. There are many fractal procedures (such as Perlin noise) capable of creating terrain data, however, the term "fractal landscape" has become more generic.

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