File:Sandpile group identity on 1024x1024 grid.png
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Русский: Нейтральный элемент в группе песчаной кучи сетки 1024×1024. Золотистый цвет соответствует 3 песчинкам в клетке, фиолетовый — 2, зелёный — 1, чёрный — 0. Если прибавить нейтральный элемент к любой возвратной песчаной куче, то после осыпания куча примет прежний вид. Для многих бинарных операций нейтральный элемент устроен очень просто (так, это ноль для сложения чисел и единица для умножения), но модель песчаной кучи — классический пример группы, в которой нейтральный элемент устроен сложно. В изображении видны регулярные и фрактальные структуры, однако их присутствие пока не объяснено и не доказано.
English: The neutral element of the Abelian sandpile group on the 1024×1024 grid. Golden color corresponds to 3 grains in the cell, purple to 2, green to 1, black to 0. If one adds the neutral element to any recurrent sandpile, that sandpile will return to its original form after stabilization. For many binary operations, the neutral (or identity) element is very simple (e. g., it is zero in the case of the addition of numbers, or unity in the case of the multiplication), but the sandpile model is the classical example of a group which has a very complex neutral element. One can see some regular and fractal structures in the image, but their presence has not yet been explained or proved. |
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| Source | Own work |
| Author | colt_browning |
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I, the copyright holder of this work, hereby publish it under the following license:
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 22:56, 6 April 2019 | | 1,024 × 1,024 (141 KB) | Colt browning (talk | contribs) | User created page with UploadWizard |
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