TITLE: Visual illustrations of circle packing theorem?
QUESTION [8 upvotes]: Circle packing theorem states:
For every connected simple planar graph G there is a circle packing in the plane whose intersection graph is (isomorphic to) G.
Paper Collins, Stephenson: A circle packing algorithm describes an algorithm for obtaining circle pack corresponding to a given planar graph.
However, I tried searching internet for images of resulting circle packs, and I could hardly find just a few. Those that I found had some unusual beauty in them. I suspect whole beauty of such circle packs is still not discovered.
I would like to know if somebody tried to generate circle packs corresponding to some known classes of planar graphs, like these:



or similar?

Some rare visual examples that I found on internet.:

REPLY [2 votes]: I have computed circle packings in various special cases taking advantage of symmetry.
However, I have not implemented circle packing in full generality.

The US graph is featured in a review of Hyperbolic Geometry by Cannon, Floyed, Kenyon and Parry.  Square tilings are another geometric object associated with planar graphs.


It's hard to find good implementations of circle packing.  Even we had some, the software is slowly going out of date.  At least, a theory is pinned down in some papers:

The convergence of circle packings to the Riemann mapping that any graph has circle packings leads to a proof of the Riemann Mapping theorem 
On the convergence of circle packings to the Riemann Map
Approximation of Conformal Structures via Circle Packing
Wikipedia has many interesting references as well.