The wavelet synthesis approach I use here is based on a comment I read, in passing, from a paper I can't remember. The basic technique is to generate random coefficients in wavelet space, with higher frequency components at reduced amplitude, then perform the inverse wavelet transform to get the original heightfield. I believe the lacunarity of the resulting surface is nominally 2.0, but you can change the scaling at any particular level of the transform. The character of the surface can be changed by changing the wavelet filters, scaling factors, or random number distributions. An example applet using this technique can be found here. This applet is based on a Java port of The UBC Imager Wavelet Package, which is in the public domain.
I still haven't seen any papers documenting the details of this technique, so if you have, please send me the references.
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