摘要

 

本圖形使用SageMath創作。

摘要

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]

授權條款

我，本作品的著作權持有者，決定用以下授權條款發佈本作品：

此檔案採用創用CC 姓名標示 4.0 國際授權條款。

您可以自由：

• 分享 – 複製、發佈和傳播本作品
• 重新修改 – 創作演繹作品

惟需遵照下列條件：

• 姓名標示 – 您必須指名出正確的製作者，和提供授權條款的連結，以及表示是否有對內容上做出變更。您可以用任何合理的方式來行動，但不得以任何方式表明授權條款是對您許可或是由您所使用。

https://creativecommons.org/licenses/by/4.0CC BY 4.0 Creative Commons Attribution 4.0 truetrue

1. ↑ A visualization of the Hopf fibration by Niles Johnson