Mathematicians prove two-dimensional billiards can perform universal computation

Researchers Eva Miranda and Isaac Ramos proved that a two-dimensional billiard system can simulate a universal Turing machine, meaning one ball moving among fixed walls can reproduce any algorithmic computation. Their construction maps a program's memory and state onto regions of a table, with corridors and walls directing the ball through each computational step. The result, published in the Proceedings of the National Academy of Sciences, also transfers a fundamental limit from computer science to physical motion: no algorithm can always determine whether such a trajectory will eventually reach a designated finishing region. The construction is theoretical rather than a practical computing device.