[wcerfgba]

I'd like to see this for smaller n, to see if there are motifs or patterns, which can be used to implement memoisation like Hashlife (https://en.m.wikipedia.org/wiki/Hashlife), or to reveal new formulas for exploring Collatz sequences with.

[Fibra]

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.

[JadeNB]

> 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.

[wcerfgba]

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

[Fibra]

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

[johngossman]

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