Now that I see Fred's bitmap, I see that the squares are more-than-50%-white near one diagonal and more-than-50%-black near the other. So presumably the effect kicks in once my eye and brain start noticing local luminosity. I feel less mystified. Thanks, guys! Jim On Wednesday, July 13, 2016, Dan Asimov <dasimov@earthlink.net> wrote:
I can't believe we're actually discussing this.
The "squares" near the big X visible in the mod 2 picture are misshapen squares.
This is immediate upon magnifying the image.
That's more than enough to make the X visible.
—Dan
-----Original Message-----
From: James Propp <jamespropp@gmail.com <javascript:;>> Sent: Jul 12, 2016 9:06 PM To: math-fun <math-fun@mailman.xmission.com <javascript:;>> Subject: Re: [math-fun] Checkerboard effect
"Processing issue"? Meaning (computer) image processing, or (human) visual processing, or what?
Jim
On Tuesday, July 12, 2016, Richard Howard <rich@richardehoward.com <javascript:;>> 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:;> <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:;> <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?)
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