This is an open question: What is this fractal? It’s a method for filling a 2D plane with circles in an orderly way – circles made of circles, all the way down. There are published examples of similar systems, like the Apollonian Gasket, the Kleinian Groups, Indra’s Pearls, but I’ve never seen this particular arrangement before, and I’ve been looking for over ten years. Is this a trivial variation on something already known? Or a new and undiscovered thing? I have no idea. I found it while doodling in math class.
Update: It’s an “orbit of a circle under a Kleinian group generated by two Mobius transformations (one elliptic of order 4, one parabolic)” explanation (PDF)