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Natural Number Guy

I've been researching Collatz function for many months.. This is my own Collatz formula after lots of twiddling:

$f(n)=\lceil n-\frac{n(-1)^n}{2}\rceil$

I have an "hybrid" Cellular Automaton that simulates $(3n+1)/2$ (when odd), and $n/2$ (when even)-sequences, and Im trying to find out if I can prove wether the trajectories are divergent or reaches the trivial cycle: 2$\rightarrow1$. I use a lattice in two dimensions and see that local behaviour of a Transition Function that use two time-states can reduce some obstacles and possibly shred a light on this.

Logic, binary arithmetic, Cellular Automata are some of my current tools.

I was good at math in College, but that is all I have as formal education.

Collatz Conjecture is easy to understand, but difficult to prove.

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