3 ms·
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
by wcerfgba 2y ago
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 https://en.m.wikipedia.org/wiki/Hashlife), or to reveal new formulas for exploring Collatz sequences with.
- Fibra 2y agoGood 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.
- wcerfgba 2y agoExactly, so I'm wondering if it's possible to detect those smaller patterns in the bigger ones?
- Fibra 2y agoI'm not sure. I'll explore it a bit. Feel free to fork it and explore it yourself!
- johngossman 2y agoWarning: 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
- JadeNB 2y ago> 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_data https://en.wikipedia.org/wiki/Collatz_conjecture#Empirical_d... , for example, 27 meanders for quite a while before reaching the inevitable cycle.