The frequency synthesis approach to terrain synthesis is based on the observation that fractional Brownian motion (fBm) generates curves and surfaces that look a lot like coastlines and mountains. Because fBm noise has a well defined power spectrum, random frequency components can be calculated fairly easily, and the inverse Fast Fourier Transform then converts the frequency components into altitudes. An example applet using this technique can be found here.
Because frequency synthesis uses the Fourier transform, terrains generated by this method will wrap around both horizontally and vertically. This is fine if you want to seamlessly tile a surface, but it can be a problem if you are trying to generate a small area. You can avoid this wraparound problem by generating a larger heightfield and discarding areas near the edge, but this requires extra work.
Frequency Synthesis - John Beale's GFORGE & HF-Lab
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