3x +1 Problem: The BEST Visual Pattern of the Collatz Conjecture

In this video, the long-sought visual pattern in the Collatz conjecture is presented. With the discovery of this never-before-seen visual pattern, a new way has opened up to solving this 80-year-old conjecture.

(i) the discovery of the long-sought visual pattern in the Collatz Conjecture
(ii) the link between the Collatz conjecture and prime numbers, and
(iii) the proof that the conjecture contains no non-trial cycles.

[awebmate]

Indeed an interesting visualization of the Collatz structure.

[johndickinson]

Something I found to think about: there are triangles of twins( numbers one apart in the Collatz)a represents the top number of the triangle and below it is a+1 and the restriction is a+2 is prime.Twins are vertical in these triangles and reach a connection in the same number of moves as the rest of the twin ex: 20, 21 both reach 16 after 3 iterations. I’m not sure why 144, 145, and 146 have this behavior, reaching 94 after several moves. The triangles “start” with a(2^n -1)+(a-2), where the start are the values on the left. PS. a=-1 is an exception but is a triangle . What happens in the middle and on are that when you apply the Collatz sequence to it the twins and connections form. I think I am the first to find these “Collatz Triangles” and that they are helpful to the proof. There are patterns with a+1= 0 and 2 mod4 but I’ll leave those for someone to figure out. -Isaac D.

[fabianreid]

Here is a geometric equivalent to the Collatz function deduced from the spiral: If x is a nonnegative integer and x is passed through (3x+1)/2 if x is odd, (3x)/4 if x is a multiple of 4, and (x-2)/4 otherwise, then after a finite number of iterations, the output will be 1.

[AlamarMeraglim]

No matter where you begin your JOURNEY it ends with the ANOINTED "ONE "
JESUS 🎉 woohoo 🙌🎉

[StreamlineCarry]

Nice video!
Do you have a way of writing an expression for the sequence pattern at 7:37?
If you could find some structure in that sequence then you would REALLY have something important.

[hillaryclinton]

I asked this question.. plotting on coordinates other than xy.. the minute I heard of the conjecture.. nice to know someone has do one this. Now do it with i

[MonsterPianoPlayer]

Your number of "106 to be exact" iterations(what I call Equations) for the Number 41 is INCORRECT.
The exact number of Equations is 109.
Plus there is no need to write 4, 2, 1 twice as 4, 2, 1 is a Loop. Just write it ONCE. Then add up the number of equations.
Another Note: You wrote down "106 to be exact"(cream color text on a blue background) but in your list of Numbers(black text) there are 112 of them.

Enjoy your Day!
MonsterPianoPlayer

[pt]

google for "consists of two parts. The first, shows that if an integer can be iterated through the Collatz conjecture to one, it is the equivalent of the condition that it can be presented as a certain equation. In the second part"

[WWsoftwareradio]

if the index i starts at 0

i mod 4 = ...
0 -> negative numbers -0 -1, -2 ..
1, 3 -> positive numbers 1, 2 ...
2 -> the number which last appearances index is the smallest

that's the pattern right?
looks fun, gonna work me through the series ;)

[bigglesby]

What about 9. Or any other odd not of form 6x+1

[TymexComputing]

How i can tell from the sequence that the radial line from 0 will then be in between 5, 6 and later between 21, 22 i can see its between two consecutive numbers... Oh i can see it now - the sequence contains the extra values duplicated :)

[goutambaid]

5:47
What if my number is neither 6x+1 nor 6x-1? Like 33

[sebastiankarlsson]

Interesting pattern, but its not the first or only pattern discovered about the iterations of the collatz function. I wouldnt call it "THE pattern".

[gastonfernandomurillopluas]

This is a two-center spiral? Because I find it works best with a 4-center spiral.

[mohamedelmatal]

I'm not anglosaxone so i find some difficulties to understand your proof and specifialy you don't put caption
If you have the proof on pdf format that will better for me
Because i'm excited to show youur fauts

[tahamuhammad]

Congratulations
1- Dear Taha Muhammad, Congratulations! Your content "Collatz Sequence" has been approved and is now openly and freely available on Cambridge Open Engage.
2- Dear Taha Muhammad, Congratulations! Your content "Euler Perfect Box" has been approved and is now openly and freely available on Cambridge Open Engage.
3- Dear Taha Muhammad, Congratulations! Your content "Fermat’s Last Theorem" has been approved and is now openly and freely available on Cambridge Open Engage.

[thatdodude]

Much easier way to prove collatz conjecture is prove if any number x will eventually reach a number smaller than x

[StefanReich]

Wait. You are claiming to have proved the Collatz conjecture?

[johnathansmith]

Bro ur so close. I've got some info for u

[lock_ray]

Cool spiral, not a proof of anything. All you have done is remove even numbers and multiples of 3, I'm sorry to break it to you but anything this simple has already been done. The only reason you couldn't find it on e.g. OEIS is because it leads nowhere and so nobody bothered to put it somewhere publicly searchable.