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Gaze following, the ability to redirect one's visual attention to look at what another person is seeing, is foundational for imitation, word learning, and theory-of-mind. Previous theories have suggested that the development of gaze following in human infants is the product of a basic gaze following mechanism, plus the gradual incorporation of several distinct new mechanisms that improve the skill, such as spatial inference, and the ability to use eye direction information as well as head direction. In this paper, we offer an alternative explanation based on a single learning mechanism. From a starting state with no knowledge of the implications of another organism's gaze direction, our model learns to follow gaze by being placed in a simulated environment where an adult caregiver looks around at objects. Our infant model matches the development of gaze following in human infants as measured in key experiments that we replicate and analyze in detail.