Bunimovich Stadium BilliardA point bounces forever inside a track shaped like a running stadium. Fire off a tight bundle of paths from the same spot and on a plain circle they stay a bundle forever; stretch the circle's cap apart into straight sides and the same bundle is flung apart, a little more with every bounce off the curved ends, until the paths share nothing but the room.Leonid Bunimovich proved it in 1974: a convex wall defocuses a bundle of nearby paths, the way a curved mirror spreads a beam, while a flat wall just relays whatever spread it already has. A circle's walls are all convex and refocus perfectly, so it stays predictable forever — but stretch in flat sides and every cap-bounce defocuses without ever refocusing, and the same billiard becomes provably chaotic despite being straight almost everywhere.