[math-fun] big sunflowers
Back in September my friend Joshua Burton sent me this email. He and I and our mutual friend Michael Larsen exchanged a few emails about the phenomenon, but we never followed up: http://www.cs.uml.edu/~jpropp/sunflowers.html (I'm sending the URL because one of the imbedded images is quite large.) I asked Josh if it was okay to share this problem with others, and he replied: "By all means, share! The first to-do, I think, is to redo the work independently of the Mma engine, to confirm that the moire patterns are real, and not artifacts of some tool-specific rounding issue. If it's real, I guess the next thing is to come up with some numerical measure of the anomalous behavior of a big sunflower, as a function of N. That, or an actual clue what's going on." Jim Propp
Hello, Yes, this is the pixel problem, it is caused by the square grid of the image made of pixels. For example, when you draw lines that are close together on a pixel screen you get also Moiré patterns, http://www.plouffe.fr/simon/distributions%20modulo%201/imagepages/image50.ht... Now the image of the sunflower and the Moiré is a mixed effect between the natural occuring spirals and the 'closeness' of the points which causes the pattern, and of course : what is the formula or name of this pattern is a good question, Best regards, Simon Plouffe Le 22/03/2012 07:08, James Propp a écrit :
Back in September my friend Joshua Burton sent me this email. He and I and our mutual friend Michael Larsen exchanged a few emails about the phenomenon, but we never followed up:
http://www.cs.uml.edu/~jpropp/sunflowers.html
(I'm sending the URL because one of the imbedded images is quite large.)
I asked Josh if it was okay to share this problem with others, and he replied: "By all means, share! The first to-do, I think, is to redo the work independently of the Mma engine, to confirm that the moire patterns are real, and not artifacts of some tool-specific rounding issue. If it's real, I guess the next thing is to come up with some numerical measure of the anomalous behavior of a big sunflower, as a function of N. That, or an actual clue what's going on."
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Is there a good place to read about the mathematics of Moiré patterns? Jim On Wed, Mar 21, 2012 at 11:18 PM, Simon Plouffe <simon.plouffe@gmail.com>wrote:
Hello,
Yes, this is the pixel problem, it is caused by the square grid of the image made of pixels.
For example, when you draw lines that are close together on a pixel screen you get also Moiré patterns,
http://www.plouffe.fr/simon/**distributions%20modulo%201/** imagepages/image50.html<http://www.plouffe.fr/simon/distributions%20modulo%201/imagepages/image50.html>
Now the image of the sunflower and the Moiré is a mixed effect between the natural occuring spirals and the 'closeness' of the points which causes the pattern,
and of course : what is the formula or name of this pattern is a good question,
Best regards, Simon Plouffe
Le 22/03/2012 07:08, James Propp a écrit :
Back in September my friend Joshua Burton sent me this email. He and I and our mutual friend Michael Larsen exchanged a few emails about the phenomenon, but we never followed up:
http://www.cs.uml.edu/~jpropp/**sunflowers.html<http://www.cs.uml.edu/~jpropp/sunflowers.html>
(I'm sending the URL because one of the imbedded images is quite large.)
I asked Josh if it was okay to share this problem with others, and he replied: "By all means, share! The first to-do, I think, is to redo the work independently of the Mma engine, to confirm that the moire patterns are real, and not artifacts of some tool-specific rounding issue. If it's real, I guess the next thing is to come up with some numerical measure of the anomalous behavior of a big sunflower, as a function of N. That, or an actual clue what's going on."
Jim Propp ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
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