The KnotPlot Site

a chain of circles

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

a chain of circles

decorative swish knot

Knot Pictures

another decorative swish knot
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 a knot have been updated or created as of 8 December 2020.

Help keep the KnotPlot Project alive! Click on the button below to make a donation.

Use your credit card or PayPal account (PayPal account not needed).

Various Picture Galleries

Raytraced Examples

Other pages

Pages with little or no interesting content

This section contains pages that are badly in need of updating! Or possibly deletion.


a chain of circles


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 (torus knots, 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 site for a copy. OpenGL logo

Related work

Check out these links to see related work by other people.

a chain of circles

[Torus knot]


[Fancy knot]
Robert Scharein,<>
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 committee Dr. Kellogg S. Booth, Dr. Jim Little, Dr. Nicholas Pippenger and Dr. Dale Rolfsen.

KnotPlot is provided by Hypnagogic Software.


A big thank you to Dale Rolfsen, Jonathan Simon, and Greg Buck for much inspiration and support, especially for getting me started on the KnotPlot project.

Initial KnotPlot development was funded in part by the Department 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.

infinity symbol

no symbols where none intended