The CirclePack Owl Welcome to my homepage: Ken Stephenson Professor of Mathematics Department of mathematics University of Tennessee Knoxville Twisted Pent tiling, glass by Ken Stephenson
 Research Interests: Classical Analytic Function Theory Circle Packing (see below) and Discrete Analytic Function Theory Numerical Conformal Mapping/Structures Brain Mapping CirclePack (Java WebStart)
 Pentagonal Quilt by  Mary Jo Wickliff Circle Packing 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 well-known topic of `sphere packing'  -- how many ping-pong 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:

The Zoo:

Here is a small menagerie of circle packings in the plane, the hyperbolic plane, and the sphere.

 The  CirclePack owl:  ----->

Circle Packing Software:

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 single-click experiments, and a number of circle packing data sets can be found at CirclePack

Circle Packing Bibliography:

I try to maintain a bibliography of papers on circle packing. Download the PostScriptpdf , or CP-bib.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 37996-1300
Phone: (865) 974-4330
Fax: (865) 974 6576