The CirclePack Owl 
Ken Stephenson Professor of Mathematics Department of mathematics University of Tennessee Knoxville 
Twisted Pent tiling, glass by Ken Stephenson 
Research
Interests:

CirclePack (Java WebStart)

Pentagonal Quilt by Mary Jo Wickliff 

Dodecahedral tiling, circle packing of Cannon, Floyd, Parry pattern 
My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications. (see my curriculum vita.)
A circle packing is a configuration of circles with a specified pattern of tangencies. See the examples below; the circles typically must assume a variety of different sizes in order to fit together in a prescribed tangency pattern. (It is easy to confuse this with the wellknown topic of `sphere packing'  how many pingpong balls fit in a box car  but there is almost no contact between these two topics!!)
Circle packings were introduced by William Thurston in his Notes. Maps between circle packings which preserve tangency and orientation act in many ways as discrete analogues of analytic functions. Moreover, work flowing from a 1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circle packings. Circle packings are computable, so they are introducing an experimental, and highly visual, component to research in conformal geometry and related areas. Circle packings are also useful in graph embedding and have interesting connections to random walks. Some links to related work:
Here is a small menagerie of circle packings in the plane, the
hyperbolic plane, and the sphere.
The CirclePack owl: > 





Cortical cartography
using the discrete conformal approach of circle packings, by Monica Hurdal and Ken Stephenson Paper from Science Direct (2.5MB pdf file) 

Circle Packing: A
Mathematical Tale, by Ken Stephenson, Amer. Math. Soc. Notices (cover article), Dec. 2003. Download the pdf file (13 pages, 4.2 Megabytes) 
Curvature Flow in
Conformal Mapping, by Tobin Driscoll, Charles Collins, and Ken Stephenson Download the PostScript file (23 pages, 3.75 Megabytes) 


Approximation of
Conformal Structures via Circle Packing, by Ken Stephenson Survey paper, Computational Methods and Function Theory 1997, Proceedings of the Third CMFT Conference, World Scientific, 1999, pp 551582. Download the postscript file (32 pages, 2 megabytes); view Illustrations 

Circle Packing and Discrete Analytic
Function Theory, by Ken Stephenson Survey: Handbook of Complex Analysis, Vol. 1: Geometric Function Theory, Chapter 11, Editor Kuhnau, Elsevier, 2002 Download the postscript file (40 pages, 2 megabytes); view Illustrations 

Quasiconformally flat mapping the
human cerebellum, by P. Bowers and M. Hurdal and K. Rehm and D. Rottenberg and K. Schaper and K. Stephenson and D. Sumners Download the postscript file (8 pages, 1.5 megabytes) 
A Probabilistic Proof of
Thurston's Conjecture on Circle Packings, by Kenneth Stephenson Rendiconti del Seminario Mate. e Fisico di Milano, LXVI (1996), pp. 201291. Download the pdf file (66 pages, .28 megabytes); view Illustrations 

A "Regular" Pentagonal
Tiling of the Plane, by Philip L. Bowers and Ken Stephenson Appeared in AMS ejournal Conformal Geometry and Dynamics, Vol 1, (1997), 5886. Official download for subscribers; preprint download of PostScript file (30 page, .5 megabytes); view Illustrations 

A Circle Packing Algorithm
, by Chuck Collins and Kenneth Stephenson Computational Geometry: Theory and Applications, 25 (2003), pp. 233256. Download , gzipped postscript file (24 pages, .5 megabytes) 

Geometric Sequences of
Discs in the Apollonian Packing, by Dov Aharonov and Kenneth Stephenson Algebra i Analiz, Russian Academy of Sciences, dedicated to Goluzin, Vol 9 (1997), pp 104140. Download the postscript file (42 pages, .19 megabytes); view Illustrations 


Circle
packing: experiments in discrete analytic function theory,
by Tomasz Dubejko and Kenneth Stephenson Experimental Mathematics, Vol 4 (1995), pp. 307348. Download the postscript file (50 pages, .8 megabytes); view Illustrations 
The Java Version 1.0 of CirclePack is now available and should run on any platform with Java 1.6++. Information, CirclePac.jar (8.7 Mgb), prepared "scripts" for singleclick experiments, and a number of circle packing data sets can be found
at CirclePack
I try to maintain a bibliography of papers on circle packing. Download the PostScript, pdf , or CPbib.bib version (as of December 2002). I would appreciate any suggestions for corrections and/or additions and any references to related work.
Ways to contact me:
Kenneth Stephenson, (kens "at" math.utk.edu)
Department of Mathematics, Univ. of Tenn., Knoxville, TN
379961300
Phone: (865) 9744330
Fax: (865) 974 6576