.... After my first 1/2 a year's work on the conjecture, I came to a place of humility. I had learned for myself just how hard a math problem the Collatz Conjecture really is. I learned that I could not force this wild untamable beast into any kind of a "cage" made of logic. It was never going to do what I wanted. It was never going to listen to me.
I had to listen to it.
What kept me so entranced with the problem was that I could see the patterns in the Stopping Times Graph and the Max Value Graph, even if I could not understand them. Somehow miraculously there was a logic to this Collatz Wilderness, even if I could not understand it analytically.
I decided finally, after all these months, to try an altogether different approach; a much more quiet humble one. I decided to take off my "mathematician hat", so to speak, and analyze the Collatz patterns as though I were some other kind of scientist, a zoologist or biologist perhaps. Were a zoologist
tasked with studying the movement patterns of zebras, would they not be foolish to expect to find rock solid equations and formulae? Just because something is hard to study analytically, does that mean the thing cannot be studied? I decided to investigate the patterns of the Stopping Times Graph and the Max Value Graph as thoroughly as I possibly could, quantitatively, qualitatively, anything at all that I could find. The goal had become
to explore this strange uncharted wilderness as thoroughly as I could.
To do this I was going to have to learn a programming language. I chose Python, for its exceptional speed and for the ease with which it fluidly handles extremely large numbers. The goal of mine was to build a small armada of Python programs, like little space probes, and send them out into the Collatz Wilderness to explore, study, and photograph every aspect of the problem, gathering TONS of data... exploring many parts of the problem humanity has never looked at.
I knew just where to start looking...