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,
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