Re: [math-fun] Moire patterns
For a fun time (or maybe a headache), point your browser at http://www.nap.edu/openbook.php?record_id=2267&page=115 and then jiggle your scrollbar up and down. Then stop. Then jiggle. Then stop. Then jiggle. Can anyone explain to me what's going on in one's visual system when one does this? Jim Propp On Thu, Apr 9, 2015 at 11:41 PM, James Propp <jamespropp@gmail.com> wrote:
Three years ago, Dan Asimov wrote (as part of a math-fun thread with the subject line "big sunflowers"):
I was also about to mention the same book.
In fact, the author, Isaac Amidror, has written a second volume, "The theory of the Moiré phenomenon. Vol. II" as well as a 2nd edition of the first volume, now called "The theory of the Moiré phenomenon. Vol. I".
According to Math Reviews, these are considered the definitive reference on the Moiré phenomenon.
Also, the same guy has coauthored a recent paper:
Isaac Amidror & Roger D. Hersch (2010): Mathematical moiré models and their limitations, Journal of Modern Optics, 57:1, 23-36,
which I have downloaded and which looks quite readable.
I still haven't gotten around to looking at Amidror's book, but I did look at the online table of contents at http://diwww.epfl.ch/w3lsp/books/moire /prefaceKluwer.html (thanks, Thane!), and I also leafed through Amidror's article with Hersch, and one thing that frustrated me was the apparent absence of a framework for limit-objects.
I was expecting that, just as there are graphons in graph theory and varifolds in geometric measure theory, there'd be some sort of limit-objects that ordinary Moire pattern pictures converge toward (though perhaps one would want various notions of convergence here, depending on what features of the Moire patterns one wishes to understand in the limit).
As far as I can tell, Amidror has no interest in devising such an artsy 20th/21st century infrastructure; he just gets his hands dirty in the details of specific Moire patterns, using Fourier theory in a very 19th century way. (But I've only skimmed; maybe I'm missing key features of Amidror's approach.)
I'd be interested in more abstract approaches to the question "In what sense do Moire patterns converge?", since they'd be relevant to things like the Abelian Sandpile Model and the Rotor-Router Model that I think about from time to time; for such models one sees a variety of effects at a variety of scales, with mesoscopic effects that are quite different from both the macroscopic effects and the microscopic effects, and it's a challenge to devise the right language in which one might describe these effects and formulate conjectures, let alone prove things.
Jim Propp
Hello, the eye effect of the figure remains even if we print the page on paper. Also, for currencies they use Guilloche patterns to avoid copy, these patterns where made at the time with a mechanical device. now they are computer generated I presume, Also, the Guilloche patterns where superimposed one over the other : quite difficult to reproduce correctly on old printing machines and now with scanners the difficulty resides in the Moiré effect made by the scanner over the Guilloche patterns. The Guilloche patterns are not Moiré BUT if you scan with scanner a banknote then it will create ones ... And also it will connect on the internet and reveal information about you too, the same if you open a scanned banknote with Photoshop it will do the same : I know I tried it ! , I was making big 'fake' gray scales 100$ canadian bills for my students : giving them 1 if the answer was correct, they found the game stupid at first but with time they enjoyed that little game. Best regards, Simon Plouffe
To my surprise I perceive a somewhat fleeting and weak impression of rotation when simply moving my head relative to the screen. WFL On 4/10/15, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello, the eye effect of the figure remains even if we print the page on paper. Also, for currencies they use Guilloche patterns to avoid copy, these patterns where made at the time with a mechanical device. now they are computer generated I presume, Also, the Guilloche patterns where superimposed one over the other : quite difficult to reproduce correctly on old printing machines and now with scanners the difficulty resides in the Moiré effect made by the scanner over the Guilloche patterns. The Guilloche patterns are not Moiré BUT if you scan with scanner a banknote then it will create ones ... And also it will connect on the internet and reveal information about you too, the same if you open a scanned banknote with Photoshop it will do the same : I know I tried it ! , I was making big 'fake' gray scales 100$ canadian bills for my students : giving them 1 if the answer was correct, they found the game stupid at first but with time they enjoyed that little game.
Best regards, Simon Plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
hello, Me too, I thought first it was caused by the square grid of my screen, this is why I printed it : the same effect. Simon Plouffe
James asks what's going on inside (unexpectedly) our eyeballs/brains to produce the apparent rotation. Here's my half-baked possible explanation. Consider the images on the retina of concentric circles moving relative to the eye. Unless their centre happens to lie directly on the line of motion, these are not circles: they are slightly elliptical, with axes which are rotating. Successive frames then interfere to produce fringing, which rotates in sync. Although individually each change is tiny, Fourier analysis by the visual system reinforces the effect to perceptible level --- as happens with other similar effects invovling motion past regular railings, etc. Fred Lunnon On 4/10/15, Simon Plouffe <simon.plouffe@gmail.com> wrote:
hello,
Me too, I thought first it was caused by the square grid of my screen, this is why I printed it : the same effect.
Simon Plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Fred Lunnon -
James Propp -
Simon Plouffe