I've managed to rearrange the collatz conjecture into a formulae and was wondering if I'm going in the right direction?
The Formulae:
$y=\left(3\left(\operatorname{mod}\left(x,2\right)x\right)\right)+\left(1\left(\operatorname{mod}\left(x,2\right)\right)\right)\ +\ \left(\frac{x\left(\operatorname{mod}\left(x,2\right)\ -\ \left(\left(\operatorname{mod}\left(x,2\right)\right)\right)\ +\ \left(\left(\operatorname{mod}\left(x+1,2\right)\right)\right)\right)}{2}\right)$
I've graphed this out and it works out to following the conjecture. However, I have no idea how to prove the x->...->4->2->1 cycle, although it's very evident in the graph. Could anyone point me in the right direction?
Your formulae is just a rendering of the Collatz map.
It produces the following sequence: $$0,4,1,10,2,16,3,22,4,28,5,...$$
See https://oeis.org/A006370.
Im not sure if you are going into the right direction, since yours is a more difficult to comprehend formula. But of course manipulating the Collatz function is a way to learn and understand the underlying mechanics of it. What do you mean its evident in the graph? Visualizing the Collatz graph in on itself is not a proof.
By the way your formula would become:
$$\frac{xw}{2}+v$$
where
$$x(z-z+w) = xw$$
and
$$w=3xz$$