I’ve got to take a break from the stripey stuff for a little while. This is circling back to the circles. I’ve taken the mapping I’ve been using from the inside of a sphere to the set of all circles, lines and points on the plane and combined them. This is what I was aiming for from the outset of this experiment, I’ve just taken a few detours getting here. I’m still trying to figure out if I can use these images or the best techniques to render the objects, or even which sets of transformations even work well for these images.
The core of the approach is tying back the relationships between fractals and parameter spaces. Given the mapping from a subset of 3 dimensional space to simple geometric objects on the plane, we can use that to map distributions of points on that subset to distributions on the simple geometric objects of the plane. I’m trying to figure out if I can make anything pretty with that, and can I exploit it to make anything meaningful out of those images. So here is a random walk through these spaces.