  The ability of Gaussian noise to induce ordered states in dynamical systems
is here presented in an overview of the main stochastic mechanisms able to
generate spatial patterns. These mechanisms involve: (i) a deterministic local
dynamics term, accounting for the local rate of variation of the field
variable, (ii) a noise component (additive or multiplicative) accounting for
the unavoidable environmental disturbances, and (iii) a linear spatial coupling
component, which provides spatial coherence and takes into account diffusion
mechanisms. We investigate these dynamics using analytical tools, such as
mean-field theory, linear stability analysis and structure function analysis,
and use numerical simulations to confirm these analytical results.
