I wasn’t aiming for something this sparse, or this kind of vertical pattern, but it turned out like a more refined version of some of my other experiments. This method is interpolating a function that resembles a Dirac delta function centered at 1/2, the other lines are reflections of that central spike.
I can’t say I’m a huge fan of these, but I’m playing around with colors and the rendering. Â Right now they just seem pretty Â for pretty’s sake. Â I think I’m waiting around for inspiration on how to put these to good use. Â These are generative and then just selected to save as an image. Â Enjoy!
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.
One of the most popular images I’ve developed (I’ve no idea what verb to stick here) is this basic geometric op art style piece. Â I was just using a very simple mask to test out using differential equations to generate families of curves. Â It’s grown on me, and I’m starting to put some more images together in a similar style. Â This is the first of what I hope is a very fruitful series.
The first images I generated used first order differential equations, which have the nice property that the curves never cross. Â However, it severely limits the shapes that can be produced as each point has one and only one direction through it. Â Bumping up to second order added multiple directions through a point as an option, and it turns out some of those crossings can end up looking pretty sharp.