@STxAxTIC I find your pdf very illuminating... more than other pages that of the table of sequence generated using the Collatz algorythm.
If we see the positive integer family as the set of number going from 1 to +infinite or in different words we see them like an halfline
and if the division is a movement towards the 1 and the multiplication is a movement towars the +infinite, then we can see the Collatz conjecture as this affirmation: starting form any point of the half line we always arrive at point 1 if we divide by 2 the even numbers (if we go towards 1 of half of number's distance from 1) and if we multiply by 3 and we add one (if we go towars + infinite of 3 times the number's distance from 1 and we add 1 unit) getting an even number if the number is odd
here a graphic rapresentation on the table taken from your PDF [ You are not allowed to view this attachment ]