Collatz conjecture cycles [4K] [modular arithmetic]
Collatz conjecture sequence (modulo P) where P is a prime with primitive root 2
using modulo P will guarantee that we can construct a perfect modular cycle map
I am going to split the screen into four sections with the same perfect modular cycle map
on all four sctions. but every section will show a different Collatz sequence cycle
1 → 4 → 2 → 1 ...
−1 → −2 → −1 ...
−5 → −14 → −7 → −20 → −10 → −5 ...
−17 → −50 → −25 → −74 → −37 → −110 → −55 → −164 → −82 → −41 → −122 → −61 → −182 → −91 → −272 → −136 → −68 → −34 → −17 ...
Important Notes
The trivial 0 → 0 cycle will not be included but you can still see it
because it will always be at the center of the map
I know that it is also possible to construct a perfect modular cycle map using (mod 3^n)
(this way you can exclude 1/3 of the values from that perfect modular cycle map)
but that is for another video! that is why i did not include the (mod 3) cycle as well
Music by JMC-ID from Pixabay
Mandarin Calmly Music