lots-o-touching-links
I’ve added a new gallery of images. Rather than just working through more random 2 point fractals, this is a gallery of them with just a simple setup. One rotation and one purely scaling transformation. Even with this restriction I was surprised at the number of distinct shapes I was able to generate.
One of my favorite series is the circles of circles which is built of circles all the way down. I had never seen these before and they have a beautiful simplicity, plus I find the whole concept mind blowing. At least with the cantor set construction, it stuck with line segments dividing into a “dust”. The circles of circles, especially the linked ones just throws me for a loop, even though it isn’t really any different than any of the other shapes.
The other two series that stood out were the scalloped and spiral/pinwheel series. There was just something about how clean and effervescent the shapes came out that I really liked.
Nice. I used to play around with this stuff (IFS, fractals, chaotic systems) in a Windows program years ago. I’ve always wanted to port it to HTML5/canvas, which sounds like what you’re doing. What I did then (and what you seem to be doing now) is to keep the attractors moving and responsive to sliders, as opposed to just generating still pictures.
You can push this IFS-style rendering to do Julia-type fractals and Kleinian group limit sets as well, as this (ancient) gallery shows – http://www.brainjam.ca/fractals.html.
Thanks. I love your site, especially the sound of chaos, and the non-Euclidean visualizations. I’ve had the audio idea on the back burner for the past 15 years or so, but never learned an audio API to make it happen. I can’t wait to see what you do with it, and a saw this was just released: https://github.com/jussi-kalliokoski/audiolib.js#readme
I have some test pages using WebGL to render linear IFS fractals using the julia type approach. It’s nice, but it renders the detail on the exterior of the fractal, and I don’t find the results quite as visually interesting. I’m just starting to put together test code to compute the full inverse tree of the point to shade both the interior and exterior points.