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