Sledding on a Bumpy Slope: Chaos and Strange Attractor

downhill position of Poincaré diagram

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This Demonstration shows a sled sliding down a mogul-covered hill. The mogul pattern is periodic: 10 meters long downhill by 5 meters wide across the hill. The accompanying Poincaré diagram shows the range of points of cross-hill velocity versus position as the sled proceeds downhill. The points for the Poincaré diagram are taken at 10-meter downhill intervals; you can vary this position within the 10-meter range of the repetitive pattern. In chaotic paths, the Poincaré pattern shows a limited range of values, and even more so in a nonchaotic path.