  Power-law noises abound in nature and have been observed extensively in both
time series and spatially varying environmental parameters. Although, recent
years have seen the extension of traditional stochastic partial differential
equations to include systems driven by fractional Brownian motion, spatially
distributed scale-invariance has received comparatively little attention,
especially for parameters defined over non-standard spatial domains. This paper
discusses the generalization of power-law noises to general spatial domains by
outlining their theoretical underpinnings as well as addressing their numerical
simulation on arbitrary meshes. Three computational algorithms are presented
for efficiently generating their sample paths, accompanied by numerous
numerical illustrations.
