File:Hopf Fibration.png
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Summary
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| Description |
English: Some points on the two-sphere and their corresponding fibers in the Hopf fibration. Hopf fibers are projected to a 3-ball by a variant of stereographic projection.
Español: Algunos puntos en la 2-esfera y sus fibras correspondientes en la fibración de Hopf. Las fibras de Hopf están proyectadas a una 3-bola usando una variante de la proyección estereográfica. |
| Date | |
| Source | Own work |
| Author | Niles Johnson |
Summary
This image is part of an animation created with SageMath. Further information at http://www.nilesjohnson.net/hopf.html "The Python-based mathematics program Sage was used for determining the fiber parametrizations and keeping track of all the animation data. Sage provides an interface to the ray tracing system Tachyon, and this is what produced the individual frames. The music was edited with Audacity. To stitch the frames into an animation, I used FFmpeg, a full-featured program for working with audio and video in a broad range of codecs. The frames for this animation were rendered on the high-powered machines made available by Jonathan Hanke at the University of Georgia, and I'm extremely grateful for this support. Raytracing the final product took 24 modern processors about 40 hours."[1]
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:44, 6 July 2020 | | 9,920 × 8,816 (31.49 MB) | Nilesj | cropped out some white space |
| 12:35, 6 July 2020 |  | 10,800 × 10,800 (32.25 MB) | Nilesj | higher resolution version of the original | |
| 19:00, 31 October 2012 |  | 737 × 665 (405 KB) | Nilesj | User created page with UploadWizard |
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