The method for generating fractal surfaces is based on the following idea. First the original texture is separated by color projection along the main color directions. The result of this operations are gray pictures describing the fluctuation along the axis.
Transformation is calculated.
By computing the average value over the amplitues on a fixed radius you get a one dimensional spectra that is symmetrical over rotation. This spectra ist approximated by a summation of gaussian functions. Transformation you get the resynthesized images. Now overlay this gray pictures by a linear combination of the new axis and you get the synthesized texture.