Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds

TL;DR

This paper presents a spectral synthesis method using Laplace-Beltrami eigenfunctions to simulate fractal surfaces on manifolds of any dimension, extending fractional Brownian motion models.

Contribution

It introduces a generalized spectral approach for simulating fractal surfaces on arbitrary manifolds, broadening previous fractional Brownian motion techniques.

Findings

Successfully generates fractal surfaces on various manifolds.

Handles manifolds with and without boundary.

Provides implementation details and examples.

Abstract

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.