Spherical or plane-bent CAPs?

The past few weeks in my video blog, I've played with the concept of taking our current understanding of elliptical CAPs and translating them into 3-D shapes. I dubbed the concept "spherical CAPs" but I'm now starting to question if it's either accurate or actually descriptive of the concept. Here's why:

I've blogged before about the mathematics of CAPs (or at the very least referenced what someone else wrote on the topic ;) and have finally come to understand that the concept is rooted not necessarily in the idea of having a repeatable "move" per-se, but in the idea of having multiple segments that incorporate different moves to form new patterns--hence "assembly patterns." This now explains to me why elliptical CAPs are referred to as such: they are collections of ellipses that are assembled into larger patterns.

So are the "spherical" patterns that have been showing up in my videos made up of spheres? Nope, they're named via the opposite approach: the fact that the path of the hands trace out the wireframe of a sphere. If, for example, one where to approach using two of the 3D CAP patterns I've played with and transition between two 3D shapes, one could then make the argument that you'd created an assembly pattern made up of multiple spherical shapes, but also by that logic, moving between repeatable patterns with unit circle hybrids would likewise qualify. Perhaps we could approach the concept of a "unit sphere" the same way--not as a basic unit of movement but as a basic element of 3D CAP patterns.

Food for thought...