Chaotic systems are the paradigmatic examples of how a system can be trivial to understand but still intrinsically unpredictable. After a certain amount of time (τ ), the state of a chaotic system becomes fundamentally unpredictable without collecting new data. The moment that new information is collected (e.g., position and velocity of a particle with some precision) the system is predictable for another τ before gradually receding beyond the information horizon. Billiards with curved boundaries are the classic example of such systems. Although the ballistic trajectories are trivial to trace, tiny changes in initial conditions will lead to qualitatively different positions and velocities after a small number of reflections.