Any cool works, websites, or videos with Collatz inspired art? Reply to this post
Collatz tree as a sea anemone
3n+1 extended to complex numbers
XKCD - classic!
Any others?
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Aron Frishberg plots “steps to reach 1” (actually the remainder of that divided by 6). As expected, kinda looks like TV snow! But with a color TV.
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a bunch of random 50-digit start numbers (in binary) all descending to 1, scaled to fit the same vertical space…
Hello, from time to time I create pixel art related to the Collatz Conjecture.
X3-1 is represented by Gaby, she owns the red numbers
X3 is represented by Nully, she owns the yellow numbers
X3+1 is represented by Stacey, she owns the blue numbers
I hope you guys like the artwork!
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Pixel art + Modular arithmetic = Awesome!
Really original, love it
This image from the wikipedia page is quite pretty: File:Collatz conjecture tree visualization.png - Wikimedia Commons
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I have a feeling something is fundamentally wrong. Not with the conjecture itself, but the way we are using it. I think it has rules like the basic rules for math: 4+4/2 = 6 and not 4. In this case we keep dividing our answer without looking at which formula produced that answer.
So hereby my User Manual for the Collatz Conjecture and some of the loops that would be wrong or right.
I like the art, but I sincerely hope this is all wrong. So please prove this if you can. Else we might have been chasing shadows ever since the conjecture was introduced.
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I seriously wonder what the pattern or patterns will look like if you use the user manual I previously posted
You might be interested in this representation of collatz sequences based on Langton’s Ant. Likewise, there are some variations of this scheme, across a couple other posts in my blog.
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@Fibra This is awesome! What a super-interesting way to visualize parity sequences. (Thanks also for bringing up Langton’s ant, which I’d never heard of before.) I wonder if you tried 5n+1, especially with start numbers like 7, where the trajectories are presumably infinite.
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I haven’t. Feel free to play around with such examples with this script which will return the trajectory of the ant over time for a given starting n. The few tweaks would merely be to change 3n+1 to 5n+1 in the while loop. Albeit one might need to cap the frame length of the run, if such n doesn’t halt.
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I also have covered the 1D version of this scheme for instance in Collatz's Tape (along with with a version of it where the tape also affects collatz dynamics), which might be also interesting.
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