Peripheral vision provides a less faithful representation of the visual input than foveal vision. Nonetheless, we can gain a lot of information about the world from our peripheral vision, for example in order to plan eye movements. The phenomenon of crowding shows that the reduction of information available in the periphery is not merely the result of reduced resolution. Crowding refers to visual phenomena in which identification of a target stimulus is significantly impaired by the presence of nearby stimuli, or flankers. What information is available in the periphery? We propose that the visual system locally represents peripheral stimuli by the joint statistics of responses of cells sensitive to different position, phase, orientation, and scale. This "textural" representation by summary statistics predicts the subjective "jumble" of features often associated with crowding. We show that the difficulty of performing an identification task within a single pooling region using this representation of the stimuli is correlated with peripheral identification performance under conditions of crowding. Furthermore, for a simple stimulus with no flankers, this representation can be adequate to specify the stimulus with some position invariance. This provides evidence that a unified neuronal mechanism may underlie peripheral vision, ordinary pattern recognition in central vision, and texture perception. A key component of our methodology involves creating visualizations of the information available in the summary statistics of a stimulus. We call these visualizations "mongrels" and show that they are highly useful in examining how the early visual system represents the visual input. Mongrels enable one to study the "equivalence classes" of our model, i.e., the sets of stimuli that map to the same representation according to the model.