Human infants actively forage for visual information from the moment of birth onward. Although we know a great deal about how stimulus characteristics influence looking behavior in the first few postnatal weeks, we know much less about the intrinsic dynamics of the behavior. Here we show that a simple stochastic dynamical system acts quantitatively like 4-week-old infants on a range of measures if there is hysteresis in the transitions between looking and looking away in the model system. The success of this simple three-parameter model suggests that visual foraging in the first few weeks after birth may be influenced more by noise and hysteresis in underlying neural mechanisms than by how infants process visual information after a look begins.