Can the Collatz conjecture also be interpreted as behaviour, transformation of number of form $N\equiv 3(\textrm{mod }4)$ to the form of $N\equiv 1(\textrm{mod }4)$
Because integers of the form $N\equiv 3(\textrm{mod }4)$ can be later always only ones be divided by $2$. Number of form $N\equiv 1(\textrm{mod }4)$ have much more diversity.
$3,7,11,15,19,23,29,35, \ldots, N \equiv 3(\textrm{mod }4) $(distance $4$ between numbers)
using $(3n+1)/2$ or applying $+2,+4,+6,\ldots$ turns into
$5,11,17,23,29,35,41,47,\ldots, N \equiv 1 (\textrm{mod }4)$ or $3$ (50%) (distance $6$ between numbers)
again using $(3n+1)/2$ or applying $+3,+6,+9$ turns into
$8,17,26,35,44,53,62,71,\ldots$ (distance 9 between numbers), $N(\textrm{mod }4)$ is various.