Problems Involving Syracuse

Let it be known that I am no mathematician. I know little to nothing about math, my arithmetic is sloppy, I never cared much for math in school and, it is only recently that I am discovering that this stuff has any sort of value outside of aggregating your bowling averages, and doing your taxes. In fact I am rather annoyed that no one bothered to explain to me when I was more impressionable that this stuff is real. That is accurately describes the interaction of all activity in the universe. There are also some really beautiful, and deeply mysterious things at play here. An example that I have recently applied my rudimentary programming knowledge to is the so called Syracuse Problem, or Collatz Conjecture, the Hailstone Sequence, and the Ulam Conjecture to name but a few. The problem remains unsolved to this day. The conjecture is that regardless of the starting point, all sequences put into this wormhole will finish the same; specifically 16, 8, 4, 2, 1. The formula is such:

for (n):
if even: n/2
if odd: 3n + 1

This process is repeated until ultimately reaching 1. The reason it is unsolved is because it is still unknown weather all positive integers will eventually trail off the same. It is however presumed they will. I wanted to see what some of these sequences might look like, so I fired out some code and got the following in return. In the first, red circles indicate odd values, while outlined circles indicate odd in the second example which tracks multiple integers. The Y position simply adds 1 to itself until the sequence terminates.