[math-fun] Greedily packing disks in a sector
What do you get if you start packing unit disks in a 72-degree sector of the plane, placing each successive disk as close as possible to the corner? Some sort of quasiperiodic structure? Jim Propp
Is the procedure uniquely defined? In fact, if some result is quasi-periodic, I suspect it won't be ... WFL On 12/19/12, James Propp <jamespropp@gmail.com> wrote:
What do you get if you start packing unit disks in a 72-degree sector of the plane, placing each successive disk as close as possible to the corner? Some sort of quasiperiodic structure?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If there are ties, then it would make sense to follow all the branches for a while to see if they reconverge. Of course the asymptotic packing can't be unique, but it might be unique module mirror reversal. (Is there software that makes problems like this easy to play with? If I had to write the code myself it'd take me days to do, and there's a good chance that my code would have mistakes that I'd miss.) Jim On Wednesday, December 19, 2012, Fred lunnon wrote:
Is the procedure uniquely defined?
In fact, if some result is quasi-periodic, I suspect it won't be ... WFL
On 12/19/12, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
What do you get if you start packing unit disks in a 72-degree sector of the plane, placing each successive disk as close as possible to the corner? Some sort of quasiperiodic structure?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If there are ties, then it would make sense to follow all the branches for a while to see if they reconverge. Of course the asymptotic packing can't be unique, but it might be unique module mirror reversal. (Is there software that makes problems like this easy to play with? If I had to write the code myself it'd take me days to do, and there's a good chance that my code would have mistakes that I'd miss.) Jim On Wednesday, December 19, 2012, Fred lunnon wrote:
Is the procedure uniquely defined?
In fact, if some result is quasi-periodic, I suspect it won't be ... WFL
On 12/19/12, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
What do you get if you start packing unit disks in a 72-degree sector of the plane, placing each successive disk as close as possible to the corner? Some sort of quasiperiodic structure?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Fred lunnon -
James Propp