Gijs van der Giessen definitly, and by the way: Happy Birthday Bob Ross...

***How many apples you have in an **#Apple_Tree**, so many **#Dead_Nodes_Will_eat***** ***I appreciate your work in generally . I think here you are making a mistake. **#Collatz_Conjecture** into negative axes isn't a Collatz Conjecture , and if you follow my work , can see for what. Anyway as promised , I solved Collatz Conjecture via **#Murgu_Lemas** **#Collatz_Conjecture_Logical_Dead_Nodes_Lema** **#Eternal_Triad** (which demonstrated every odd Integers , except Logical Dead Nodes and **#Collatz_Perfect_Numbers_Dead_Nodes** but with a dual sense), and **#Collatz_Conjecture_Murgu_Formulas** --- **#Collatz_Conjecture_Solved** as promised. I worked on it in any **#Rest_Time_Times** , then take it as it is , but is solved at: " **kzfaq.info/get/bejne/iLZ1eqmLx7S7YnU.html** "*** ***Anyway , at this time **#Beauty_Math_Curiosity** (**#Mathematics_Curiosity** ) is **#Murgu_Conjecture_Vicious_Redundancy** " **kzfaq.info/get/bejne/rNRje5qSutPKpJ8.html** " for which I don't have dare to start over, because don't have time, but because maybe never will can demonstrate that have to had only 3 roots (1,5,17)***

~ Happy syntax errors ~

Thank you!

Thank you.

Someone has messed with prng algorithms. Either that or has an inherent talent for them and should go dethrone marsaglia, the current rnjesus

I've only recently happened-across this corner of iterative functions... IMHO, you've hit the nail on the head with 'binary'... That 4-2-1 loop (surprisingly 'octal') is, I believe, KEY to understanding this whole business (but I don't have the math skills to express it as a 'proof'... Notice that seeding the function with zero ALSO goes into this loop (3 * 0 + 1 = 1)... All 8 octal bit patterns (0-7), as seeds, are contained within the lowest 3 bits. Adding another 3 bits (seeds ranging 0 - 63) and the trajectories will, like the infamous 27, occasionally take off toward the clouds, but will eventually decay to the loop... Add another 3 bits (0 - 255, total 3 octal digits) and some trajectories go even higher... BUT, they all decay to the loop again. There are interesting observations to be made about 'intervals' between some of the longer trajectories (ones that go for long excursions before landing on a previously 'used' value that is part of a path toward inevitable decay... 4n+1 points to some interesting seeds, like 32 - (4(1)+1) a.k.a. 32 - 5, our old friend "27"... Hmmmm So, it's been shown that all values of the highest octal digit value combined with all values of the middle octal digit value combined with all values of the lowest octal digit value eventually collapse to the 4-2-1 loop... Conceptually, trying 2 "middle" octals between the high octal and the low octal (ie 12 bits or 0 - 4095) should (will) express similar behaviour. Try 3 "middle" octals (total 15 bits) ... same thing... Viewing the intermediate values in binary, it soon becomes apparent that 'bubbles' of multiple zeroes form, and the lowest octal is desperately trying to drag the value lower (4 is even and 2 is even, so divide and divide... The bits have been shifted to the right twice, and stratospheric numbers come back down to the troposphere... Often a 'bubble' of 6 zeroes forms tantalisingly close to the LSB... A few more steps and the entire value collapses several orders of magnitude. It's fate is sealed and destiny a certainty... Veritasium recently claimed all numbers to 2^68 have been tried, and, for all variations of those 68 bits, all numbers eventually 'collapsed'... Excuse me for thinking this... I recognise that infinity is a very, very distant ceiling, but even with my 32bit explorations (lots of bit pattern variations) the decay begins after not too many iterations of the function... There are 'rallies' along some paths taken, but the conclusion seems inevitable... With nothing but this evidence and intuition, I'm happy to conclude that "bubbles will form" quickly enough (in the rightmost bits) that will reverse any excursion toward the stars, and the strange attractor of "4-2-1" is the fate of all positive integers that enter into the Collatz Conjecture...

Collatz(x) {return x&1 ? x+x>>1+1 : x>>1;}

Thank you! and Thank you for the support!

That is a great observation! It's like Daniel is the Bob Ross of coding! edit: I just watched the first in this series and saw that KZfaqr István Horváth ​already made the Bob Ross connection.. ​

Where you people got this emoticon..I need one

Yay, share what you make!

wrong

Indeed!

@@TheCodingTrain Thank you for keeping inspiring us every day...in the Cabaña ;) Gracias Maestro!

Coding in northern Ontario

P.S: A third of my tea evaporated due to boiling while I wrote the comment

now that I know a quick image search gives some really good results of graphing techniques for different visualizations besides the common graphs.

Looking forward to it!

@@TheCodingTrain yes 😄 I haven't made my own variations for a while because I haven't got the time to do so. 😄😄 but i will also do the #TeamTrees one and this one too ❤ #TeamTrees

Yes, that is a good point, thanks for the feedback! I think the floating things are just dust particles, the sun was shining directly in!

yep!

Thanks for this feedback!

yeah exactly, I'm pretty sure just changing that back will fix thr entire image

More likely just a warm coat and layers. . need an orioles beanie!

i believe in order to add it to MS Word file (.docx) it has to be in .emf format.... do we have this format as an option in Proccessing or P5.js ??

@@ahmedhassanahmedhassan6495 You can save it as a .png file by using 'save("collatz.png")' where he shows you to put 'endRecord();' in the code. This means you don't have to put 'beginRecord(PDF, "collatz.pdf");' and 'endRecord();' in the code! This means it doesn't look as good when you zoom in, so if .docx documents accept .svg files, you can save it as 'collatz.svg' instead, I think.

oh! Yes, that makes sense!

Thank you for the generous support!