 The discrete version can be defined on any graph, usually a lattice in "d"-dimensional Euclidean space.The continuum version is defined on R"d" or on a bounded subdomain of R"d".It can be thought of as a natural generalization of one-dimensional Brownian motion to "d" time (but still one space) dimensions; in particular, the one-dimensional continuum GFF is just the standard one-dimensional Brownian motion or Brownian bridge on an interval.