Comment by exasperaited

This is very cool, but somewhat confusing to the eye, because you are actually demonstrating the movement of a point along a path, while visualising it with a cube whose orientation doesn't change when it feels like it should.

The point that is moving is in the centre of the cube. But the cube's orientation is fixed in global space.

So the cube's orientation relative to the path of the spiral/helix is not quite the same as its orientation relative to the path of the straight line.

Your mission, should you choose to accept it ;-)

https://en.wikipedia.org/wiki/Frenet–Serret_formulas