My Multi Dimensional Collatz Conjecture

Описание: correction : at 19:10 when I said 200 steps, I meant to say 2,000 steps.

GitHub : https://github.com/CharthuliusWheezer...

references
Collatz Conjecture : https://en.wikipedia.org/wiki/Collatz...

OpenSCAD Website: http://www.openscad.org/
OpenSCAD Documentation: https://en.wikibooks.org/wiki/OpenSCA...

A viewer mentioned that I didn't actually make any conjectures about the system so here are a few :

In the cases where the dimension of the starting vector is at least 2.

1 : If we define a class of vectors as a permutation of a value x and/or 0’s. All vectors in a class will converge to the same cycle for the non-negative integers. These could be referred to as the diagonals which essentially reduces to the regular Collatz Conjecture.

2 : There are starting vectors that do not converge and infinitely vary. As in there is at least 1 starting vector of integers that never converges to a cycle. Which means none of the vectors
in it’s sequence are listed twice.
I would separate this into two cases, i: where all values in the vector are strictly non-negative, or strictly non-positive, and ii: where there can be any values positive, negative, and/or zero.

3 : There is no constant time algorithm to rigorously determine whether an arbitrary starting vector will converge to a cycle or not.