[math-fun] Draft of my July 2017 blog post
I started writing a new draft titled "Swine in a Line" (a small piece of the picture that relates chip-firing to number representation systems) and would love to get your feedback. I plan on publishing it on Monday. Sorry for the shortness of notice. (Making the last two Barefoot Math videos took longer than I thought on account of equipment problems plus my being in England on holiday for over a week.) In addition to seeking the usual suggestions for how to make things clearer and livelier, I'm also seeking good links to good short web-pages on sandpiles and chip-firing that are in the same spirit as this article and aimed at the same readership. (I'm not planning to include a link to my Notices article with Levine on sandpiles; aside from it being too technical, it veers too much in the direction of fractal patterns, and although I touch on this indirectly via the Numerphile video, that's not really what I want to focus on here.) Please leave your feedback here: https://mathenchant.wordpress.com?p=1784&shareadraft=59690647cdd0e (keeping in mind that if you don't sign your comment I won't know who you, with the consequence that I won't be able to ask follow-up questions that your comments may elicit). Title: Swine in a Line Beginning: Last month I launched a new venture similar to my Mathematical Enchantments blog: a YouTube channel I'm calling Barefoot Math. The first few videos are about a game I invented that I call Swine in a Line. It's a game with an easy-to-describe but not-so-easy-to-find winning strategy, and the challeng... Read more: https://mathenchant.wordpress.com?p=1784&shareadraft=59690647cdd0e Thanks, Jim
Just two remarks and a question about the sand piles. See https://oeis.org/A249872 for the number of moves to reach a steady state. This is independent of the way the updates are made. Q: is the final configuration also always the same? This is a nice problem to do on an FPGA: as expected, the performance is very good, for the 1000 x 1000 instance wall clock time is about 40 times that of a modern CPU and the number of cycles spend is less by a factor of 3000. This is a nice student project IMO (the student needs to be experienced with FPGA design). Best regards, jj * James Propp <jamespropp@gmail.com> [Jul 15. 2017 16:52]:
[...] Read more: https://mathenchant.wordpress.com?p=1784&shareadraft=59690647cdd0e
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Joerg, Yes, for each n the steady state is independent of the way updates are made, as is the number of updates. In fact, the number of times each individual site "fires" is predetermined. This is the confluence phenomenon I alluded to, and it is proved using the Church-Rosser / Newman / diamond lemma. I'd say more but I have to finish and publish the piece! Jim On Monday, July 17, 2017, Joerg Arndt <arndt@jjj.de <javascript:_e(%7B%7D,'cvml','arndt@jjj.de');>> wrote:
Just two remarks and a question about the sand piles.
See https://oeis.org/A249872 for the number of moves to reach a steady state. This is independent of the way the updates are made.
Q: is the final configuration also always the same?
This is a nice problem to do on an FPGA: as expected, the performance is very good, for the 1000 x 1000 instance wall clock time is about 40 times that of a modern CPU and the number of cycles spend is less by a factor of 3000. This is a nice student project IMO (the student needs to be experienced with FPGA design).
Best regards, jj
* James Propp <jamespropp@gmail.com> [Jul 15. 2017 16:52]:
[...] Read more: https://mathenchant.wordpress.com?p=1784&shareadraft=59690647cdd0e
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Joerg Arndt