The Collatz Conjecture... but in Binary

Let me explain the “3x+1” mystery (the Collatz conjecture) and show some cool shortcuts that happen if we interpret it in binary, as well as some extensions like including negative numbers!

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This episode was filmed by Carlo Trappenberg (plus a few scenes filmed by Jonathan Ruchlis). It was directed and edited by me (Domotro) and I also made the music in the soundtracks. And here's a link to the public domain fractal image I included near the end:
https://en.wikipedia.org/wiki/Collatz...

A small correction: near the end, when showing the negative number patterns, I had 1-2-4 written above those as an example of the positive loop, but 1-2-4 is in backwards order with the way I drew the arrows (arrows+error=errows?). That was meant to refer to the normal 4-2-1 loop (which could also be written as 1-4-2 or as 2-1-4) that was in the earlier portions of the episode.... There's also a few little typos: I misspelled "result" as "resut" one one whiteboard, and I accidentally typed "and my" twice on one of the credits whiteboards. Whoops.

Special thanks to Evan Clark and to all of my Patreon supporters:
Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, and Fredrik!...
(Also thanks to my cats Sage, Dandelion, and Sassafras! Can you spot all 4 of Dandelion's catmeo appearances in this episode?)
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If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first:    • You Can Now Mail Me Things to Put in ...  
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709

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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com

DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.