File:Hopf_Fibration.png
From Wikipedia, the free encyclopedia
Original file (9,920 × 8,816 pixels, file size: 31.49 MB, MIME type: image/png)
This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
Warning | The original file is very high-resolution. It might not load properly or could cause your browser to freeze when opened at full size. | Open in ZoomViewer |
---|
DescriptionHopf Fibration.png |
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]
Licensing
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- 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.
Items portrayed in this file
depicts
some value
31 October 2012
image/png
6d2b7e8ad0fcce64a6481f8101698b012ebd2258
33,020,639 byte
8,816 pixel
9,920 pixel
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 |
File usage
Global file usage
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on de.wikipedia.org
- Usage on es.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on ko.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on uk.wikipedia.org
- Usage on www.wikidata.org
- Usage on zh.wikipedia.org
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Horizontal resolution | 28.35 dpc |
---|---|
Vertical resolution | 28.35 dpc |
File change date and time | 12:38, 6 July 2020 |