When coding XOR patterns I was amazed at the complexity from eg a simple (x^y)%3
When hand drawing/calculating it, I get a bit of an intuition why...
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@noneuclideandreamer@mathstodon.xyz
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Drawing Links!
Isometric Paper is fun. 😁
#mathart
There is probably an easier way to get to this output than implementing a 3-component Reaction-Diffusion pattern. But it wouldn't feel the same...🤗
Not sure whether one can see what's going on here...
Pacman Disassociating
#mastoart
Jasmin Stitch - it was messy fumbling all the way, no getting into the flow... 🙈
f(x,y)=( x / (y ^ ( x - y ) ) ) % 2040
Full Version: https://youtu.be/K_JypACeC9E
Where would we expect this too look interesting?
/ is integer division, so the bigger the divisor, the more pixels are gonna get crushed into the same value.
The picture will thus look interesting, where (y ^ ( x - y ) ) is small.
^ is bitwise xor: If you write both inputs in binary you get the output in binary by setting a digit to 1 iff the corresponding digits in the inputs are different. So the xor output is small if its inputs are similar (the more significant digits match)
So we expect an interesting picture for y~x-y, or 2y~x.
New xor pattern generalization dropped! For each pixel (x|y) write x and y in base 3, then add the corresponding digits of x and y mod 3.
Here we have purple for f(x,y)%4==0
Let me show you these Recursive Graphs my kid (12years old) came up with!
Explanation/Making-Of video: https://youtu.be/sX1gz13-_Xc
Location dependent Reaction-Diffusion.
Full Version: https://youtu.be/yeGOwMkbvo8
#mathstodon #mastoart
Whipped up some quick code to find terminating rules and gave them to the kid to draw!
Icosahedral Stereograph!
I made a making-of video for this crocheted cellular Automaton:
https://youtu.be/YjW4R5sGvdk
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@ddrake@mathstodon.xyz Top left is (0|0). For each square I take it's coordinates as x and y. Yeah mod 3, but I only colored the value 0!
Hyperbolic Truncated Icosahedral Fractal
Dodecahedral Stereograph!
For this Month's High-resolution Render for Patrons of Level Square and up I replugged and coded up the xor-variation in a juicy watermelon palette!
Full Resolution:25600x14400
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@chrisamaphone@hci.social Yeah but I warn you, it's quite addictive... so many rules to try...
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@ngons@mathstodon.xyz Thanks! 🤗
Besides the panning I vary the color assigned two each value (0 to 17):
I slowly rotate the hue and, more importantly, I rotate 3 bumps of saturation around.
I noticed that showing the rainbow of all values actually takes away from the image, because they blur each other out. So I dim some to black.
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@loopspace@mathstodon.xyz Yeah the colored bottom makes it weird.
And the perfect angle of the last doesn't work...
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@shironeko@fedi.tesaguri.club I mean the angle of the last one is so that you basically only see one face...
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@0x10f@tech.lgbt Lovely!
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@ddrake@mathstodon.xyz Your math is correct, but not sure about your conclusion.
The output of (x^y) can be any integer, only after the %3 it is reduced. But I think the pattern would look mostly the same if I did (x^y)%3==1 instead. And for (!(x^y))%3==1 also.
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@toerror@mastodon.gamedev.place @Slackermanz@mathstodon.xyz There is a lot on YouTube!
@slackermanz@youtube.com
My Patrons can on my May Theme!
The Options are:
-Hyperbolic Manifolds
-Unplugged
-Multineighbourhood Cellular Automata
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@yomikoma@weirder.earth Yup, it's essentially choosing a subset of the edges of a graph that simply connects all vertices.
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@gilesgoat@toot.wales No, we have rules depending on neighborhoods of various scales and shapes.
@Slackermanz@mathstodon.xyz has done some amazing stuff with them.
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@kirch@tilde.zone Oh yeah that's an extra dimension! 🤗
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@bit101@mstdn.social Interesting... I think of the cubes as behind the grid...
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@ddrake@mathstodon.xyz I mean it's just two colors of squares, can't be that expensive. 🤷 😇
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@yomikoma@weirder.earth Are you perhaps crossing your eyes? I calculated it so that the cubes are behind the screen
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@mike805@noc.social I guess it's my own flavor of vector graphics. 😁
I think I implemented left-wall-following, not right. 😇
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@Insanitree@infosec.exchange @0x10f@tech.lgbt You can get both from an L-System I think.
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@shironeko@fedi.tesaguri.club Hmm, that of course highly depends on the size of your screen...
My little squares are 0.5cm. I assumed for my calculations an eye distance of 8cm and a eye-screen distance of 32cm. But intererestingly it seems to kinda work for different zoom factors.
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@SvenGeier@mathstodon.xyz The colors are always fully saturated, I work with hue and brightness.
In the beginning I have one spectrum wrapped around the possible values, it shifts but also tightens, so we have several rainbows.
Bit then I have a Sine function on the brightness as well, always highlighting 6 equidistant hues. It's shifting through the colors.
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