The Collatz Conjecture is one of the most insurmountable math problems on the market today. The famous mathematician Paul Erdös once state, “Mathematics is not yet ready for such problems.” I am not sure I believe this anymore. I have spent the last three years intensely researching the Collatz problem. It began innocently enough – Fueled by curiosity, I constructed a small armada of Python programs and launched them out into the Collatz Wilderness to explore new aspects of the problem and bring back data and images. This new data revealed many patterns and principles of Collatz space that have been hidden up to this time.

One particular one of my Python machines was programmed to study the relative sizes of the Collatz Branches, and its findings were shocking. I’ve discovered that if you zoom out and view the seemingly random and chaotic happenings of Collatz Space on a global scale, that a fascinating kind of stability and uniformity seems to be taking place. My Python engines have brought back extensive experimental evidence suggesting this hidden global stability is in fact a property of the \(3x+1\) Collatz Space. My senior thesis covers this result and shows why, if I can prove it true, the divergence half of the Collatz Conjecture follows from it as a corollary.