Governance by those who do the work.

Wednesday, October 10, 2018

The Lamb-Oseen Vortex and Paint Marbling


Just published The Lamb-Oseen Vortex and Paint Marbling on arXiv.

The image to the left shows the decay with time of the Lamb-Oseen vortex (starting from an impulse of circulation at the center point).


The image to the right shows the same vortex, but with exponentially increasing time.  The rotational shear propagates to larger and larger orbits while the center returns to rest.  While this animation returns to its original position, it could come to rest at any angle controlled by the magnitude of the initial circulation.

More about mathematical marbling.

7 comments:

  1. I’ve looked through your blog, and through the Voluntocracy site and your CSAIL page, and I could not find a link to the software used. Is it available, perhaps on Github or someplace similar?

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    1. It is a PostScript file converted to gif by ImageMagick "convert anim3.ps anim3.gif". I have put a copy at http://people.csail.mit.edu/jaffer/Marbling/anim3.ps

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    2. Thanks, but I meant the program incorporating your marbling algorithms, the one that generates the PostScript files. Did you ever release that, whether as a commercial product, freeware/shareware, or open-source?

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    3. PostScript is a programming language. I created the PS file with a text editor. It has the algorithms in it.

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    4. Just looked at the PS file. Oh—wow. That’s amazing.

      I’m trying to convert the file on my own system (Ghostview froze waiting for ghostscript to process the file, so who knows?) and then I’ll try to puzzle out how to customize the pattern. Oh, look, ImageMagick took less time than it took me to write up this comment. Again, wow.

      The GUI interface shown in https://youtu.be/ZgVbIaKhC_4, was that a generator for the PostScipt files, or was that a different implementation?

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    5. https://youtu.be/ZgVbIaKhC_4 was created by Shufang Lu, Xiaogang Jin, Hanli Zhao, and Xiaoyang Mao using GPU on a video card. Unfortunately, their implementation was not released.

      J├╝rgen Gilg and Luque Manuel have collaborated to create the PST-marble package which makes it much easier to create your own mathematical marblings.
      https://ctan.org/pkg/pst-marble

      http://pstricks.blogspot.com/2018/09/the-marbled-paper-with-pstricks.html
      show nice examples of marblings you can create with pst-marble.

      I am developing an online tool for those who don't have LaTeX and CTAN installed on their computers.
      Will post to this blog when it is released.

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    6. Thank you so much for that CTAN link! I’m looking through the documentation now, and I think I’ll be able to make use of this. If I succeed, I’ll be sure to send you a picture of my results.

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