Billiard-Ball Computer 2D: Conservative Logic Gate

Fredkin and Toffoli's 1982 "billiard-ball model of computation" showed that ordinary conservative mechanics — hard spheres colliding elastically — can compute logic without ever erasing a bit, avoiding the k_BT·ln 2 minimum energy Landauer's principle charges any irreversible operation. This 2D simulator implements that idea with genuinely independent 2D collision mathematics: two equal-mass balls launch from the top corners along crossing diagonals, and whether they collide exactly at the crossing point is the logical AND of the two inputs. It then goes one step further than a plain AND-detector by adding two fixed circular reflectors placed on each ball's own straight-line path. Working the symmetric elastic-collision algebra through shows that a collision swaps the balls' velocity components exactly enough that each ball still arrives at its own input's reflector afterward — so the reflector readouts recover the original A and B bits even after the AND has been computed. A live kinetic-energy readout stays flat through both the collision and every reflector bounce, making the "no dissipation, no information lost" claim of conservative logic something you can watch rather than take on faith.