Extemely cool!!! Especially with all those parameters to play with, even the polynomial!!! But I am wondering if the white diagonal of slope = -1 that I am seeing (so far unchanged with all parameter combinations that I've tried) is intentional. Or alternatively: How can I get rid of it? (iMac 27"). —Dan
On Jan 13, 2016, at 12:44 AM, Christian Lawson-Perfect <christianperfect@gmail.com> wrote:
I've updated my code so it renders in realtime, like Gareth's, but I've found that replacing half of the colour spectrum with black makes it much easier to see the pattern. You can see that the centres of circles lie on the lines y = x*a and y = x/a, for integers a. There are also symmetries obtained by the fact that x^2=(-x)^2, y^2=(-y)^2, and (x+N)^2 is congruent to x^2 mod N, where N is the number of colours. Here's the link again: http://codepen.io/christianp/full/PZjGmV/
On Wed, 13 Jan 2016 at 05:18 James Propp <jamespropp@gmail.com> wrote:
Why do Kerry and Gareth's pictures look so different?
I gather that the latter is closer to what Dan had in mind, but the former seems to me to have a richer Moire structure.
Jim Propp
On Monday, January 11, 2016, Dan Asimov <asimov@msri.org <javascript:_e(%7B%7D,'cvml','asimov@msri.org');>> wrote:
Oh, yeah! That's exactly the picture I had in mind. Thanks so much for making it!
Now maybe some number theorist can explain the patterns.
—Dan
P.S. Though for a hexagonal pixel structure with pixels labeled via
x * 1 + y * exp(2pi*i/3)
I would want to try x^2 + xy + y^2 (with all coefficients = 1, no 2's.)
On Jan 11, 2016, at 4:30 PM, Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
On 11/01/2016 23:02, Dan Asimov wrote:
Nice! Christian, I don't know if you take requests, but:
Would you be willing to do the same thing but with 1024 or more colors, on a larger square?
Try this: http://codepen.io/anon/pen/ZQyaYm
which uses more colours, on a larger square, at one pixel per pixel, and does it using an HTML5 canvas object rather than by constructing an enormous table with one cell per pixel.
(For reasons I don't at all understand, this has stopped actually working for me on the computer where I created it -- it sits there saying "Loading" for ever and never actually draws anything -- but on another one it works just fine. My apologies if whatever I've screwed up causes it not to work for some of you too.)
The "skeleton" of the code is copy-and-pasted from some tutorial thing that obviously envisages turning this into an animation. I've experimented with making it animate but what it's doing is a bit too expensive for my taste.
If on line 10 you set colours to a smaller value (try, say, 100) more of the finer structure of the Moire fringes will be exposed.
With the default values (1024 for both), on some monitors you may see flickering in some parts of the image. I think this is not an optical illusion but the result of temporal dithering by a monitor that uses that technique to represent a larger number of brightness levels for each channel than the display is actually physically capable of.
Try replacing x*x+y*y with 2*(x*x+y*y)+x*y for a hexagonal structure.
-- g
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