The KnotPlot Site (original) (raw)
Welcome to the KnotPlot Site!
Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, an elaborate program to visualize and manipulate mathematical knots in three and four dimensions.
Download KnotPlot for Windows, macOS and Linux
Check out the mathematical knots(M) page as well to see more knot pictures. Or try some of the following examples to see some knots in a different light. The pages marked with 
have been updated or created as of 8 December 2020.
KnotPlot is now on Patreon! Help keep the KnotPlot project alive by becoming a member today!
Join for as little as a cup of coffee per month.
Various Picture Galleries
Raytraced Examples
Other pages
- Quote from Clifford Ashley
- Interactive Topological Drawing, my dissertation
- Short discussion on braid theory(incomplete).
Pages with little or no interesting content
This section contains pages that are badly in need of updating! Or possibly deletion.
- Knotted Sea Things
- Various Odd Knots, Unknot Flowers M
- Knot Diagrams from Dowker Codes (better information is available in mydissertation)
- Knots on the Cubic Lattice
- Hopf Torus M
KnotPlot features
Knots can be loaded from a database of more than 3,000 knots and links or sketched by hand in three dimensions. Also, knots may be constructed via the Conway notation or using the tangle calculator. A number of special knot types (torusknots, knot chains, Lissajous knots) may be created on the fly. Finally, new knots can be created from old knots by various tranformation tools. Using all these features allows the creation of quadrillions of different knots (and many more).
Downloading KnotPlot
KnotPlot is an OpenGL program that runs on most types of computers. Go to the download sitefor a copy. 
Related work
Check out these links to see related work by other people.
Robert Scharein,< @hypnagogic.net>
If you have comments on these pages please feel free to email them to me.
KnotPlot was part of my PhD thesis work in the Imager Computer Graphics Laboratory. The warmest appreciation goes to my supervisory committeeDr. Kellogg S. Booth,Dr. Jim Little,Dr. Nicholas PippengerandDr. Dale Rolfsen.
KnotPlot is provided by Hypnagogic Software.
Acknowledgements
A big thank you to Dale Rolfsen,Jonathan Simon, and Greg Buckfor much inspiration and support, especially for getting me started on the KnotPlot project.
Initial KnotPlot development was funded in part by theDepartment of Computer Science at the University of British Columbia (UBC/CS), the Media and Graphics Interdisciplinary Centre (MAGIC), the Pacific Institute for the Mathematical Sciences (PIMS), and the Centre for Experimental and Constructive Mathematics (CECM). The hugest of hugs to PIMS, CECM, and UBC/CS for hosting the KnotPlot pages over all these years.
Copyright © 1998–2022 by Robert G. Scharein
Unauthorized hosting of copies of the KnotPlot Site, in whole or in part, on any web server for any purpose, is expressly forbidden.
