“The synthesis and rendering of eroded fractal terrains” by Musgrave, Kolb and Mace

In standard fractal terrain models based on fractional Brownian motion the statistical character of the surface is, by design, the same everywhere. A new approach to the synthesis of fractal terrain height fields is presented which, in contrast to previous techniques, features locally independent control of the frequencies composing the surface, and thus local control of fractal dimension and other statistical characteristics. The new technique, termed noise synthesis, is intermediate in difficulty of implementation, between simple stochastic subdivision and Fourier filtering or generalized stochastic subdivision, and does not suffer the drawbacks of creases or periodicity. Varying the local crossover scale of fractal character or the fractal dimension with altitude or other functions yields more realistic first approximations to eroded landscapes. A simple physical erosion model is then suggested which simulates hydraulic and thermal erosion processes to create gloabl stream/valley networks and talus slopes. Finally, an efficient ray tracing algorithm for general height fields, of which most fractal terrains are a subset, is presented.

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