How can I make a square spiral (curve) in Geometry Nodes 3.4

Question

I used discrete curve lines connected to each other but in the end it created a boundary between them. In the picture, I added Curve to Mesh with Curve Circle

I sincerely apologize that my nodes are so messy and unclear. But basically I'm trying to Instance on Points the new Curve Lines to the end points of the original Curve Lines and rotate it $90°$.

I hope there is a way to make a single curve with a square spiral shape!

Answer 1

You can solve the task with the following setup:

Here I use a mathematical setup based purely on the index of a spline and some math nodes.

I calculate a specific position in the positive or negative range for each point on both axes.

_{(Blender 3.4+)}

Answer 2

Another approach using instancing.

The spiral is composed of 'corners':

• on the upper left part they are growing from 2, 4, 6 etc.
• on the lower right part they are growing from 1, 3, 5 etc.

The setup combines these two corner 'arrays' and merge them.