Exactly, so I'm wondering if it's possible to detect those smaller patterns in the bigger ones?

I'm not sure. I'll explore it a bit. Feel free to fork it and explore it yourself!

Warning: huge amounts of compute time have been spent trying to find a counter example to this conjecture, which almost everyone believes is true. I kept my office warm this way one winter. It has been described as a way to turn pure Platonic mathematics into heat.

Always interesting to try to visualize something though.

Ps -- I implemented hashlife one time. Still amazed someone came up with that algorithm

> Good idea. Although, from the little exploration I did with examples for small n, given the low stopping times, the behaviour was very boring. Nothing necessarily interesting. But then again, I didn't explore it exhaustively.

Long and/or large excursions can happen even for small n! As mentioned at https://en.wikipedia.org/wiki/Collatz_conjecture#Empirical_d... , for example, 27 meanders for quite a while before reaching the inevitable cycle.