A computing system and method to implement a three-dimensional virtual reality world with avatar eye movements without user eye tracking. A position and orientation of a respective avatar in the virtual reality world is tracked to generate a view of the virtual world for the avatar and to present the avatar to others. In response to detecting a predetermined event, the computing system predicts a point (e.g., the eye of another avatar) that is of interest to the respective avatar responsive to the event, and computes, according to an eye movement model, an animation of the eyes of the respective avatar where the gaze of the avatar moves from an initial point to the predicted point and/or its vicinity for a period of time and back to the initial point.