Helical Vectors

In my last post I showed how the angle of interconnected triplet of dots can be increased to introduce twist into an ordered origami.

However, this post was mostly a proof-of-concept. It didn’t bring me that much closer to figuring out the mathematics of creating a helical twist.

So, for today’s post I’m going back to basics and instead of trying to fit triangles together, I instead make an entangled double-helix of two strings of dots, with a secondary twist. Or more specifically I reduce the primary twist so that the movement of the dots is no longer linear but represented with a helical path. This is shown with the four green helical curves in the image below.

I think I haven’t made this image, at least with vectors included, before. However, it was dead simple to make.

And just for the fun of it, this is what it looks like head-on:

I’m moderately happy that I managed to make these images easily, but I know they offer limited help in me figuring out how this straight structure can be made into a helical structure. So, next I’ll try to figure out how to do that. I’ve already started preparing a lattice structure that should help me figure it out. This is how the idea stage of it looks like:

I’m not yet sure whether this approach helps, but you’ve got to begin somewhere.