algorithmic modeling for Rhino
As David said, you'd need to script to go much further with this, but if you do want to, there's a really great book all about Kleinian groups called Indra's Pearls. It has got some deep mathematics in it, but it assumes virtually no prior knowledge and it's full of cartoons and explanations in plain english and lots of pseudo-code (not a typical math book at all).
I don't know if anyone is still interested in this, but I was able to answer the original question here with a simple grasshopper definition using Hoopsnake for the recursion. The key is to use the CircleTanTanTan function.
I just wrote a post about this on my blog, here. Attached is the Grasshopper definition.