A fractal landscape is essentially a two-dimensional form of the fractal coastline, which can be considered a stochastic generalization of the Koch curve. The topological dimension 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. Since there are many fractal procedures (such as Perlin noise) capable of creating terrain data, however, the term "fractal landscape" has become more generic.
Kenton "Doc Mojo" Musgrave is considered a leading authority on fractal landscapes and his most recent computer program, MojoWorld , is one of the more convenient ways to investigate them. The core of Dr. Musgrave's work in this area centered on rendering planetary bodies from orbital heights smoothly down to the surface with adaptive level of detail. Mojoworld basically makes this process interactive for anyone with a sufficiently powerful PC. Another highly popular program in this vein is Matt Fairclough 's Terragen.
Although fractal landscapes look natural at first glance, repeated exposure brings disappointment to those who expect eroded mountains. The main complaint is that simple fractal processes do not (and perhaps cannot) mimic actual geological and weathering functions.
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