Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds
This work addresses the need for simulating fractal surfaces on arbitrary-dimensional manifolds, which is incremental as it builds upon existing fractional Brownian motion methods.
The paper tackled the problem of simulating fractal surfaces on smooth manifolds by using the spectral decomposition of the Laplace-Beltrami operator to generate random fields as series of eigenfunctions, generalizing fractional Brownian motion to multi-dimensional parameters with examples provided for surfaces with and without boundary.
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 multi-dimensional parameter. We give examples of surfaces with and without boundary and discuss implementation.