Comment by PabloRobles

We use a similar method to simulate 2D atmospheric turbulence for adaptive optics simulations in astronomy. The structure of turbulence is described by an analytical power spectral density function (classically Kolmogorov spectrum). We generate random coefficients in the Fourier space and then weight them by the PSD. After an inverse Fourier transform we obtain a beautiful draw of turbulence with the desired spatial structure.