Several techniques for fractal terrain synthesis exist. The original method for generating fractional Brownian (fBm) surface uses Poisson faulting . This method involves application of random faults having the Gaussian distribution (see Figure 1)
resulting in the statistically undistinguishable surfaces (planes or spheres). The main drawback to this approach is time complexity.
Most fractal terrain models are based on two faster methods for generating fBm: Random midpoint displacement method and Fourier synthesis.
Figure 1: Gaussian distribution.