The Collatz Conjecture and Fractals

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Published 2016-09-13

Visualizing the dynamics of the Collatz Conjecture though fractal self-similarity.
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All Comments (21)

@carykh 3 years ago

:O Those fractals are so beautiful, and the fact that the number of edges on each level of fingers describes the path 3 takes through the Collatz procedure? That's crazy!
@felinx49 7 years ago

These videos are so beautiful and insightful. Please keep making more of them!
@harrywilson1660 6 years ago

Really good video, I wasn't expecting the relationship between the number of fingers and the orbits of natural numbers!
@klebbonk4493 7 years ago

Amazing job eliminating the usual "dryness" that comes with these kinds of abstract sequences
@jacobchateau6191 3 years ago

WOW that's absolutely amazing! The way the fractal's structure indexes the recursion is splendid.
@RadioactivePretzels 7 years ago

Wow, that was a fun visualizion.. both the original number line loops as well as the fractal complex extension. Knowing you, you probably wrote both visualizations with procedural shaders? Whether you did it or not I would love to see another video of the same length just describing the tools you made and/or used to make this video!
@Graeme_Lastname 7 years ago

Informative and beautiful. A rare combination.
@mullanalle4318 3 months ago

Good work! I don't find surprises in number theory too often nowadays. New angle, and i'm a bit jealous to be honest
@mueezadam8438 4 years ago

So grateful I was able to rediscover this video, it’s a classic for me.
@xyz.ijk. 2 years ago

That was really brilliant. I hope you're following through on this and other research. I'm looking forward to finding your other videos.
@teslababbage 2 years ago

This is absolutely stunning work - well done!
@bdogwynn 7 years ago

Thank you so much for this. Thank you for demonstrating the beauty, complexity and difficulty of this problem.
@1234dck 5 years ago

brilliant. congratulations. very clear
@MathOSX 6 years ago

What a brilliant idea to extend the map into the complex field. Hopefully someone will one day use this new point of view to crack the collatz conjecture !
@famskiller8208 5 years ago

This video made me like you instantly. I am amazed how you visualized the numbers. I am fascinated by this conjecture and glad to have found your video. Keep it up
@LukePalmer 5 years ago

Really fascinating and awesome. The fractal shape analysis encoding the dynamics is amazing, I haven't seen anything like it before. Thanks!
@tzimmermann 7 years ago

Very well done, impressive!
@ethanrenckly787 6 months ago

Sir, you have answered more questions than I came here looking for answers to, and for that, you have my thanks.
@TimJSwan 1 month ago

Along with Math Kook, this is in my opinion one of the most interesting videos on Collatz for me. Thanks.
@AaronHollander314 5 years ago

Awesome! Brilliant explanation and insight.