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Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include sea-waves, smoke, foliage, whirlwind etc. We present a novel characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the “essence” of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of second-order stationary processes, we identify the model sub-optimally in closed-form. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computa- tional cost. We present experimental evidence that, within our framework, even low-dimensional models can capture very complex visual phenomena.