Collatz Conjecture from an Infinite Field Perspective

I was just thinking of the Collatz Conjecture again. So what if you took the hypothetical perspective of the infinite field, searching for a path to 1 that took an infinite number of steps, using the same 3x+1 and 2x pathways? Really this is the same equation, where infinite steps from a number in this direction means that number is the solution for the original equation, but it feels as though an entirely different set of rules/logic might be applicable, when approaching from this direction (it feels almost like a game of Guess Who, where whole fields of pathways can be knocked down at once, until one may or may not remain). As I was considering this I was also thinking of the shape of the solutions which are knocked down. If each pattern removed were color coded, for example, and then after a time you sent an equation through to navigate those numbers that remained (and imagined yourself/a ship as this equation), to see if you could intuit how to beat proceed, would one like a meteorologist be able to look at the skies and the seas of these colored patterns, the density and flow of them at one's given position, and use this sense to determine how next to explore for an answer? As there would be no hard limit to imagining starting at 1 and imagining starting at infinity, you could even toggle between these two directions to help navigate. I love this analogy, for it feels like it traverses nicely between the logical and wondrous and, even if the answer is not found, the journey may be an enjoyable one, without sights not before seen.