File:Ergodic mixing of putty ball after repeated Smale horseshoe map.jpg
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Summary
| Description |
English: First, a small (2 cm in diameter) ball was made of putty of different colors. Then it was squashed flat and both sides were photographed. Then it was folded in two, squashed, folded in two again and squashed again and then both sides photographed.This operation was repeated several times, until the ball became quite homogeneous. Every squash+fold+squash procedure is equivalent to one iteration of so called "Smale horseshoe map", so it may be said that between consecutive photographs the ball was twice subjected to Smale horseshoe mapping. In the end it was cut in half to show that the internal material is also well-mixed. Русский: Небольшой (2 см в диаметре) шарик был слеплен из пластилина разных цветов. Потом шарик был расплющен и сфотографирован с обеих сторон. Затем он был свёрнут вдвое, расплющен, снова свернут вдвое, снова расплющен и затем обе стороны сфотографированы. Эта процедура повторяется несколько раз, пока шарик не становится практически однородным. Каждая операция "сплющить - сложить вдвое - сплющить", похожая на приготовление слоёного теста, эквивалентна так называемому отображению "Подкова Смейла" - классическому понятию в теории динамических систем. Таким образом, между последовательными фотографированиями, шарик дважды подвергался отображению подковы Смейла. В конце концов, в завершение этого эксперимента, шарик был разрезан надвое, чтобы показать, что внутри шарика пластилин тоже хорошо перемешан. |
| Date | |
| Source | Own work |
| Author | Yaroslav I. Sobolev and Kamil R. Karimullin |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:22, 14 March 2014 | | 2,000 × 12,559 (4.02 MB) | wikimediacommons>Lomita | Suppression tag |
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