[ginko]

Talking about shower thoughts on Collatz visualizations..

A while ago I though of a way of structuring the collatz orbits by arranging integers in a 2d grid with odd numbers being arranged along the X axis and multiples of the power of two along the Y axis.

https://gist.githubusercontent.com/ginkgo/13121db56b65b1237e...

So essentially any odd number n and all numbers n * 2^m belong to the same group of numbers that eventually reduces to n. All that's left is the 3n+1 orbits which are shown as lines from the odd numbers.

This reveals quite a bit of structure (IMO) especially only every second odd number goes to an orbit reducing to an odd number larger than it (and it's always in the form n * 2^1) all the other orbits every 4th, 8th, 16th odd integer immediately reduce to an odd number that's lower.

Anyone seen an arrangement like this for the Collatz orbits?

[gpm]

Just wanted to chime in and say that's a really interesting visualization of the conjecture, I haven't seen it before (and I have wasted more than a few hours on this problem).

[bawana]

try this visualization https://gist.github.com/bwanaaa/4c77b33311916b230c8b1891bab4... just open it in collar and the 3d graph appears