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Summary
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| Description |
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.
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| 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]
Licensing
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
Click on a date/time to view the file as it appeared at that time.
| 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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