In this paper we explore the connection between anisotropic Gaussian fluctuations and isotropic non-Gaussian fluctuations. We first set up a large angle framework for characterizing non-Gaussian fluctuations: large angle non-Gaussian spectra. We then consider anisotropic Gaussian fluctuations in two different situations. Firstly we look at anisotropic space-times and propose a prescription for superimposed Gaussian fluctuations; we argue against accidental symmetry in the fluctuations and that therefore the fluctuations should be anisotropic. We show how these fluctuations display previously known non-Gaussian effects both in the angular power spectrum and in non-Gaussian spectra. Secondly we consider the anisotropic Grischuk-Zel'dovich effect. We construct a flat space time with anisotropic, non-trivial topology and show how Gaussian fluctuations in such a space-time look non-Gaussian. In particular we show how non-Gaussian spectra may probe superhorizon anisotropy.