Simulation enables robots to plan and estimate the outcomes of prospective actions without the need to physically execute them. We introduce a self-supervised learning framework to enable robots model and predict their morphology, kinematics and motor control using only brief raw video data, eliminating the need for extensive real-world data collection and kinematic priors. By observing their own movements, akin to humans watching their reflection in a mirror, robots learn an ability to simulate themselves and predict their spatial motion for various tasks. Our results demonstrate that this self-learned simulation not only enables accurate motion planning but also allows the robot to detect abnormalities and recover from damage.