Jim asks: << ... I've thought about switching to even more confusing families of circles, which (if they haven't been named yet) OUGHT to be called "Dionysian space-fillers". To get one of this hairy objects, start with an Apollonian gasket and begin promiscuously inverting circles in the gasket with respect to other circles in the gasket....

...

This sounds like a case of sexual inversion.... Jim: Since there are various versions of Apollonian gaskets, could you tell us exactly the one you are using to get started here? Dan <asimov@msri.org>