Thoughts from a Recreational Physicist
I like this because it includes a strong two point  linear cantor set attractor with a rotation that looks like it should be symmetric, but as your look at the details, the internals are off.  Yet, the transformations are so simple the actual symmetries reveal themselves from inspection.
This one reminded me of a fractal version of the tic marks on a ruler. Â It’s up there with the minimal spiral for one of my favorite illustrations of the self similarity of fractals. Â As they become more complex, it becomes more and more difficult to make out the relationships between the different parts. Â This one being more “one” dimensional seems to make it easier to take in.
This one feels like it is constructed out of lines rather than individual points, which seem to make the relationships less mind bending, even though the definitions only differ by a few numbers.  The moment it really sunk in that every individual point in the circles I was looking at really really was circular patterns all the way down.  I’d been looking at and computing images of various fractals for over 20 years at that point, but had never made that particular connection before.  I had to see the parts as an exact copy of the whole instead of  each one being subtly different.
This image, while not very visually interesting has a lot of accidental symmetry.
These guys use four transformations with simple rotation parameters. All I changed is the scaling factor of the two central transformations and their centers. It shows how the nature and feeling of the image can change dramatically with just a few little parameter changes.
I wanted to make something more linear, but not.
In the mean time, I’ve been playing around with angularjs, plus have been installing laminate floors in my house, and I ran into How to fold a Julia Fractal a few weeks ago.  What a fantastic use of 3d at the top of the page, though it doesn’t scroll well on any of my systems.  It’s inspired me to rethink my approach for building interactive demos, and the UI of this site.  Fun stuff ahead.
This has an almost Mayan feel getting ready for the upcoming apocalypse.