Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds

Using the spectral decomposition of the Laplace-Beltrami operator, we simulate fractal surfaces as random series of eigenfunctions. This approach allows us to generate random fields over smooth manifolds of arbitrary dimension, generalizing previous work with fractional Brownian motion with multidimensional parameter. We give examples of surfaces with and without boundary and discuss implementation.