The KnotPlot Site

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, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer (see the link below), but first you may want to look at some of the images in the picture gallery.

Note: If you are referencing this page off a CD-ROM, you are seeing a "snapshot" of the KnotPlot Site at a particular date. If you have internet access, go to the KnotPlot Site on the web. That web site, like all web sites, is constantly changing (maybe even improving).

Knot Pictures

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 15 May 2000. Those marked with an M have at least one MPEG animation.

Various Collections

Raytraced Examples

Bizarre (or not-knot-like) Examples

Other pages

KnotPlot

KnotPlot features

Knots can be loaded from a database of almost 1000 knots and links or sketched by hand in three dimensions. Also, knots may be constructed via the Conway notation or using a 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 using a number of transformations.

Downloading KnotPlot

A complete distribution of KnotPlot is included on this CD-ROM for a number of different computer types. A (probably) more up-to-date version of KnotPlot can be also downloaded from the Pacific Institute for the Mathematical Sciences website (follow the "Techno Math" link).

Related work

Check out these to see related work by other people.

[Torus knot]

Author

[Fancy knot]
Robert Scharein, <@cs.ubc.ca>
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.

Thanks to

I am considerably indebted to my committee as well as Jonathan Simon and Greg Buck for much inspiration and support.

KnotPlot development was funded by The Department of Computer Science at The University of British Columbia, The Media and Graphics Interdisciplinary Centre, and The Pacific Institute for the Mathematical Sciences.

I'd also like to thank the following for kindly acknowledging the KnotPlot Site:

Britannica
(2000)
Camel's
Knot a Braid
(1996)
San Francisco Exploratorium
Learning Studio
March 97
(mathematics)
Dr. Matrix Weird
Web World of Science
(mathematics>
Learning in Motion
April 97 issue
(mathematics)

Copyright © 1998-2000 by Robert G. Scharein


no symbols where none intended