This paper addresses the problem of modeling stationary color dynamic textures with Gaussian processes. We detail two particular classes of such processes that are parameterized by a small number of compactly supported linear filters, so-called dynamical textons (\emph{dynTextons}). The first class extends previous works on the spot noise texture model to the dynamical setting. It directly estimates the dynTexton to fit a translation-invariant covariance from the exemplar. The second class is a specialization of the auto-regressive (AR) dynamic texture method to the setting of space and time stationary textures. This allows one to parameterize the process covariance using only a few linear filters. Numerical experiments on a database of stationary textures shows that the methods, despite their extreme simplicity, provide state of the art results to synthesize space stationary dynamical texture.