Visual illustrations of circle packing theorem?

Question

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?

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Some rare visual examples that I found on internet.:

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Answer 1

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.

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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 Even we had some, the software is slowly going out of date.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.

Answer 2

If you read the very last item in the paper that you linked, you will see that the authors of that paper give a link to software that computes circle packings.