[math-fun] Checkerboard effect
Go to http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h... , hover your mouse over "modulo 2 (low res) <http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.htm#nogo>", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.) What's happening here? That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?) Jim Propp
To make life easier, here's a direct link to the image in question: http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/mod2Spiral.pn... On Tue, 12 Jul 2016 at 15:56 James Propp <jamespropp@gmail.com> wrote:
Go to
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h... , hover your mouse over "modulo 2 (low res) < http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.)
What's happening here?
That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Try relaxing your eyes as if looking at a 3-D image--I see lots of patterns and multiple diagonal lines. I suspect it is a processing issue. --R On Tue, Jul 12, 2016 at 11:41 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
To make life easier, here's a direct link to the image in question:
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/mod2Spiral.pn...
On Tue, 12 Jul 2016 at 15:56 James Propp <jamespropp@gmail.com> wrote:
Go to
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
, hover your mouse over "modulo 2 (low res) <
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.)
What's happening here?
That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?)
Jim Propp _______________________________________________ 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
"Processing issue"? Meaning (computer) image processing, or (human) visual processing, or what? Jim On Tuesday, July 12, 2016, Richard Howard <rich@richardehoward.com> wrote:
Try relaxing your eyes as if looking at a 3-D image--I see lots of patterns and multiple diagonal lines. I suspect it is a processing issue. --R
On Tue, Jul 12, 2016 at 11:41 AM Christian Lawson-Perfect < christianperfect@gmail.com <javascript:;>> wrote:
To make life easier, here's a direct link to the image in question:
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/mod2Spiral.pn...
On Tue, 12 Jul 2016 at 15:56 James Propp <jamespropp@gmail.com
<javascript:;>> wrote:
Go to
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
, hover your mouse over "modulo 2 (low res) <
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.)
What's happening here?
That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 7/12/2016 10:55 AM, James Propp wrote:
Go to http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h... , hover your mouse over "modulo 2 (low res) <http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.htm#nogo>", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.)
What's happening here?
That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?)
Most of the "squares" are actual squares that are 5 pixels on a side. However, the four regions bounded by the diagonals are slightly out of phase with each other, each shifted one pixel left-right or up-down from its neighbors. On the boundaries this results in some "squares" which are only 4-by-5 (or 5-by-4) rectangles. Along three of the diagonals, these smaller rectangles are black, so those diagonals appear lighter; on the upper-left diagonal, the rectangles are white, so that diagonal is darker. And, right in the middle, there is a single 4-by-4 pixel black "square". A magnified view of the central portion of the image (9-by-9 "squares") with grid lines added can be seen at https://imgur.com/XqSzlpY . -- Fred W. Helenius fredh@ix.netcom.com
Thanks, Fred. I've looked closely at your magnified view, and the bit-map appears to have NO exact symmetries, of either the color-preserving or color-reversing kind. I wonder what kind of code would have given rise to it? (Note that there's a white rectangle that shares an edge with a second one, that shares an edge with a third one, that shares an edge with a fourth one, that DOESN'T share an edge with the first one. There's only one feature like that, and it's white, not black. Three of the four white rectangles are 5x5 squares, and one is a 5x4 oblong.) Jim On Wednesday, July 13, 2016, Fred W. Helenius <fredh@ix.netcom.com> wrote:
On 7/12/2016 10:55 AM, James Propp wrote:
Go to
http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h... , hover your mouse over "modulo 2 (low res) < http://www.madandmoonly.com/doctormatt/mathematics/ulamSpirals/ulamSpirals.h...
", and step back. You should see a large "X" in the image. (With my glasses on, I see the "X" when I'm about five feet away from my laptop; with my glasss off, a foot will do.)
What's happening here?
That's really two questions. What is the image made of, on the pixel level? (I'm guessing that some of the "squares" are actually rectangles with aspect ratio close to 1.) And: What are my eyes and brain doing? (Why is the effect so salient from far away but invisible up close?)
Most of the "squares" are actual squares that are 5 pixels on a side. However, the four regions bounded by the diagonals are slightly out of phase with each other, each shifted one pixel left-right or up-down from its neighbors. On the boundaries this results in some "squares" which are only 4-by-5 (or 5-by-4) rectangles. Along three of the diagonals, these smaller rectangles are black, so those diagonals appear lighter; on the upper-left diagonal, the rectangles are white, so that diagonal is darker. And, right in the middle, there is a single 4-by-4 pixel black "square".
A magnified view of the central portion of the image (9-by-9 "squares") with grid lines added can be seen at https://imgur.com/XqSzlpY .
-- Fred W. Helenius fredh@ix.netcom.com
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participants (4)
-
Christian Lawson-Perfect -
Fred W. Helenius -
James Propp -
Richard Howard