Murgu 1D Array


Under Humanity Natural Law Of Copyright

& USA ISBN-978-1-63972-042-2

resulted via a Group Theory Analytic applied for

Collatz Conjecture



Infinity Marker USA Murgu Arrows



Human Intel 2024 Logical Beauty
Infinity Table2To3

Marker USA Murgu Arrow Arrays


Collatz Conjecture Lens Mirroring Infinity
limited only by our computational power , but
Legacy To Infinity DEMONSTRATED and Contained INTO
Infinity Murgu Double Linear as Arrows Down to Unity
AS
Murgu 1D ARRAY - OLD - Collatz Conjecture 1D Array

as Murgu Collatz Conjecture Pocket Map.

- Author: Physicist Ion Murgu From Ohio USA

NOTE
Murgu 1D Array is a result Of Theoretical Collatz Conjecture Solution
Marker USA Murgu Arrows

The Theory may be qualified as a Group Theory Solutions .
You can aford it at : https://collatzconjectureend.com/
In This page will present to you 2 partial arrays of Murgu 1D array handled by 2 Javascript Programs as to see Collatz Conjecture Functional Divergence
testing in first one 4000 grids , then 24000 Integers and second 8000 grids cover Integers smallers then 48000.
The name of old Collatz Conjecture 1D Array was change in Murgu 1D Array, as to avoid multiple repetitions and for distinction between Conjecture and 1D array.
Murgu 1D Array is Infinity , but as an array don't have Infinity Index, we work with parts of it every time.
Collatz Conjecture 1D Array Now Murgu 1D Array -

May Be Meter and best tester for Computational Evolution.
Play with this Interactive Web page as can help for any similar situations .

Interactive Parts will be before page-footer.
Murgu 1D Array - Interactive, Click here




Collatz Conjecture Unique Solution
Murgu Table2To3

brougt via via Theoretical Group Theory Analytic sustained by All Mathematic Rigour Demonstrations
Marker USA Murgu Arrow Arrays


obtained using :
Murgu Infinity Table2To3Functions


((2(2k+2)[1+6i]) - 1) = 3 Qi
((2(2l+1)[5+6j]) - 1) = 3 Qj

and Murgu Collatz Conjecture Grids LET's Formulas


Grouped 2 by 2 for k=l = 0 to ∞ like Arrows heading Unity
those solved Collatz Conjecture by covering
All Positive Integers Domain.


LET1i = (1 + 6i)
LDNi = (3 + 6i)
LET2i = (5 + 6i)

Will Keep also any old material about
Collatz Conjecture Unique Solution
Murgu Table2To3
and remind - if not understood yet - I am here to explain.
First Marker USA Murgu Arrow Array
which generate Collatz Conjecture Murgu Pocket Map.


All Collatz Conjecture Murgu Formulas authority over Collatz Conjecture are demonstrated.
Murgu Collatz Conjecture Inverse Method and Formulas revealed Logical Dead Nodes Propieties
1. Logical Dead Nodes do not have Up Collatz Connection.
2. For Every Logical Dead Node a Collatz Pattern started will not pass via Collatz Procedures another Logical Dead Node.
3. For every Logical Dead Node first Down Connection will be only and only an LET.
4. Do not have 2 or more Logical Dead Node for which first LET Connection to be the same.
You will see lots of Collatz Conjecture Formulas which pretend to solve Collatz Conjecture


but neither one are coming with all Math rigor demonstrations ,
but as proofs - we can't proof Infinity margin -
Murgu Table2To3 and Infinity Murgu Table2To3 , instead , including Collatz Conjecture Murgu Formulas are Demonstrated.
also Collatz Conjecture Murgu Grids is first Conditional which make
Murgu Table2To3 - Collatz Conjecture Unique Solution


Marker USA Murgu Arrow Array or Collatz Conjecture One-Dimensional Array


came as a result revelation
and for sure became All Science Good.





Above Equations for k=l will define "Marker USA Murgu Arrow"

((2(2k+2)[1+6i]) - 1) = 3 Qi
((2(2k+1)[5+6j]) - 1) = 3 Qj

and for k=l = 0 to ∞ - Collatz Conjecture Nodes Murgu Formulas
Infinity Marker USA Murgu Arrows

will reveal all
Collatz Conjectures Nodes
as Evens as Conjecture Nodes are defined as
(2t)Qi and
(2t)Qj
Above Equations as,
Collatz Conjecture Nodes Murgu Formulas
COVER all Positive Integers if add
(2)Qi and
(2)Qj

Marker USA Murgu Arrows

Validate as a Proof
Murgu 1D Array
First Proof Backed by Absolute Truths Mathematics Values


This Interactive html whish to make clear, Collatz Conjecture Functional Divergence evidence
but also to PROOF
Murgu 1D Array is dependent by our time Computational Power . That make Murgu 1D Array maybe best eternal
Computational Power Meter and Tester.


Murgu 1D Array need 2 JavaScript programs , one Array Generator and second array handler to generate Collatz Patterns .

Here we work with 2 Javascripts Handlers and are using the same Panel and the same vriables name. If in time will consider this is not best solution , we will separate tose in 2 Panels .




To make an image or idea about - One-Dimension - Marker USA Murgu Arrow Arrays - Can see first 512 elements from 12000 if make a click down on BUTTON .
not any confusions- here Collatz Murgu Formulas value are exposed in Collatz Terms then apparent loss Collatz Unicity.


anyway can see all array into Javascript
Collatz Conjecture Enclosed into One-Dimensional Array is an H-Intel Success and to hope
Not The Last One as Science yet need H-Intel.








Marker USA Murgu Arrows born
Collatz Conjecture 1D Arry
now have 8000 Grids "only" , but can be extended and for an strong server can go to 4 000 000 GRIDS or even more.
Is a result of 2 Javascript progams


Under Open Sources MIT License


And hope MIT ,or Apple , or Google , or Intel, Or CISCO, or Microsoft will offer a online server wich to use those Javascript hich to push array to maxim elements.


Here our program will have any limits as any Collatz patterns will fal out of this array.
Soon will try to extend the array , but will became heavy on generating Collatz Patterns.


We let Collatz Patterns to be revealed into an alert , as you to can check if are correct.
This was tested with Opera.




For Mathematics
Collatz Table2To3 or Murgu Table2To3
Solved Collatz Conjecture
But For Public Infinity Table2To3 or Infinity Murgu Table2To3
CERTIFY via demonstrations Collatz Conjecture Solved by Murgu Table2To3


BUT MORE THEN THAT Brought and Reveal a New Science Tool

Collatz Conjecture One-Dimensional Array
Marker USA Murgu Arrow One-Dimensional Array

Here wearing Collatz Conjecture - but - can be applied in ALL SCIENCE in approprited Issues .
Down you can test this , via generating instant Collatz Paterns.


We chose "prompt" and after "Ok" "alert" for output , as output patterns to can be copied, and or , as to can be checked without Copy.
Also any patterns will be partial as are be evolving out of our
Collatz Conjecture One-Dimensional Array
AND need extension.
Also please chose every time an Odd Positive Integer as to make the answer instant.