Ken Stephenson - Circle Packing Images

My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with a specified pattern of tangencies. 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 fitin 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 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.

Contact me if you have questions about my research, or would like to discuss any other topics.


Ayres Hall
Ken Stephenson, mathematician, circle packing research

Ken Stephenson - Circle Packing Images

My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with a specified pattern of tangencies. 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 fitin 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 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.

Contact me if you have questions about my research, or would like to discuss any other topics.

Images provided by Ken Stephenson
Dept of Mathematics - Univ of Tennessee
Site by CMS WEBS - Knoxville

Ken Stephenson, mathematician, circle packing research
Dodecahedral Tiling

Dodecahedral Tiling / Cannon, Floyd, Parry Pattern

pinwheel

Pinwheel Circle Packing Image

collage from my book

Collage from my book, "Introduction to Circle Packing:
The Theory of Discrete Analytic Functions"

lace agg, snow better

Image 1 - Lace Agg
Image 2 - Snow Better

snow cube, mixed example

Image 1 - Snow Cube
Image 2 - Mixed Example

dimer detail, carpet

Image 1 - Dimer Detail
Image 2 - Carpet


Ken Stephenson - Circle Packing Images

My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with a specified pattern of tangencies. 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 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.

Contact me if you have questions about my research, or would like to discuss any other topics.

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Ken Stephenson, Circle Packing
Dodecahedral Tiling

Dodecahedral Tiling / Cannon, Floyd, Parry Pattern

Pinwheel

Pinwheel Circle Packing Image

collage

Collage from by book, "Introduction to Circle Packing:
The Theory of Discrete Analytic Functions"

lace agg, snow better

Image 1 - Lace Agg
Image 2 - Snow Better

snow cube, mixed example

Image 1 - Snow Cube
Image 2 - Mixed Example

dimer detail, carpet

Image 1 - Dimer Detail
Image 2 - Carpet

Ken Stephenson - Circle Packing Images

My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with a specified pattern of tangencies. 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 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.

Contact me if you have questions about my research, or would like to discuss any other topics.

Ken Stephenson, mathematician, circle packing research

Ken Stephenson - Circle Packing

My primary research interests revolve around circle packing: connections to analytic function theory, Riemann surfaces, computational conformal structures, and applications.

A circle packing is a configuration of circles with aspecified pattern of tangencies. 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 fitin 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 a1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated usingcircle packings. Circle packings are computable, so they are introducing an experimental, and highly visual, component toresearch in conformal geometry and related areas. Circle packings are also useful in graph embedding, and have interesting connections to random walks.

Contactme if you have questions about my research, or would like to discuss any other topics.

Ken Stephenson, mathematician, circle packing research

Ken Stephenson - Circle Packing

A circle packing is a configuration of circles with a specified pattern of tangencies. 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 ina 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, actin many ways as discrete analogues ofanalytic functions. Moreover, work flowing from a1985 conjecture of Thurston, proven byBurt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circlepackings. Circle packings are computable, so they are introducing anexperimental, 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.

Contactme if you have questions about my research, or would like to discuss any other topics.