Visualizing Collatz
Vložit
- čas přidán 10. 04. 2017
- This is a video response inspired by Numberphile's "Collatz Conjecture in Color" • Collatz Conjecture in ...
Twitter @wadleysf
Music : Opus One by Audionautix is licensed under a Creative Commons Attribution license (creativecommons.org/licenses/...)
Artist: audionautix.com/
This is one of the best and most exciting mathematical visualizations i have seen in my life
Thank you!
I've bought the coloring book, but what I would really like to do is find the money and space to construct this in LEGO. (Yes, I am 72 years old and still build with LEGO.)
Hurry up! Lego is for up to 99 only!
I had the same idea last weekend scribbling about the conjecture in my notebook. I know I'll never have the money and the space, but I have the virtual. So let's do it however we can! :)
Build it in minecraft or in a 3d software like blender
This is truly amazing. This deserves a reference in the initial video. I know it’s impossible because this is a response, but if it were possible to add in additional content to a video after publication it would deserve it.
A work of art
Can you pls make a video about how you did this. I would appreciate that. The pattern looks so organic, well done.
Thanks, I wish I could remember how I did it! Changed computers, lost the code - but IIRC I just used python and image libraries to create snapshots, which I then stitched together using a command line script. Finally put together in iMovie.
Ok, no problem. Thank you anyways!
Excellent visualization!
This amazing indeed , Subscribed 👍
Great work!
What are the yellow points representing and how many numbers were in that final animation?
The yellow points are the peaks of the cascades back to 1. No number less than those numbers has more steps in the sequence as the rules are applied. I was interested in where they appeared in the visualization. They're sort of grouped on the edges of sets of branches, but I couldn't see any more pattern than that.
The last animation had about 992,000 points drawn. I seta maximum value of 2,000,000 allowed for any point (not all the points below 2,000,000 are drawn because their sequence back to 1 exceeds the set maximum value for the animation at some point)
wadley sf Very cool. Thank you for that. It is very interesting, even if it does boggle the mind!
Post some github project on it and/or write a corresponding shader:)
Very cool
That last part looks like the map of Australia !
The Galaxy (last one) looks like Australia :-)
Vey Under rated
Hard as I tried, I could not see any pattern whatsoever in these visualizations. Just organic looking and beautiful.
I agree - nothing jumps out at me. But it was fun doing it, glad you thought it looked good.
Great work! :) have you posted the code somewhere?
I haven't. I've had a look for it, and I seem to have misplaced it :( If I find it I'll get it posted.
what was the last visualization of? “collatz galaxy”
The last visualization is of numbers less than 2,000,000 - their tracks are plotted out back to 1. See the original method in the numberphile video linked in the description where it is well described. In that image I think about 992,000 points were considered (some exceeded 2,000,000 on their path back to 1 and were excluded).
What tools did you use to visualize this?? =)
The code to generate the frames is in Python. I then stitched the frames together using a free command line too, then reprocessed and annotated the resulting video in iMovie, as I have nothing fancier with which to do that.
@@adrianwadley472 Which lib in python did you use? What a great video, some really beautiful patterns!
@Syrian Spitfire Thanks for the question! IIRC it was PIL/Pillow to make the separate images, then as above, I did the post-processing to stitch the images together into a video file. Hope that helps.
What is so special? There are also other (bigger) circles. Maybe with the rule 4*n+2. It needs 160 numbers to repeat. And startet with 6, 3, 14.... Instead of 3 numbers with 4, 2, 1.
Good job. :)
Thank you!
سبحان الله ، علم الانسان ما لم يعلم
Pretty, but not particularly 'useful,' per se... ;) :P
**shrug**
@Michael Gmirkin Just because *we* might see no use for it *currently*, it does not proof your statement to be true.