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. Also, have a browse through the Guestbook or sign it yourself.

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 11 Feb 2003. Those marked with an M have at least one MPEG animation.

Various Collections

The KnotServer (experimental, still not too useful), : 3D interactive viewer (which can save 3D models).
Knots as radiating tubes M
More knots as radiating tubes
Decorative knots: on white, on black, goth
Fancy Knots and Links, together with Antoine's Necklace (a fractal link)
Ashley knots
Nifty Knots with Fancy Lighting
A knot zoo and assortments of torus knots with neat colours, knot chains, and knotted graphs
More torus knots and links, arranged by crossing number
Brunnian Links M
Tangle Calculator Examples
Linking Spheres in three or more dimensions
PDF and PostScript examples
Knot Carpets
Celtic Knots
3D Stereoscopic Pictures (page 1, page 2, page 3, page 4, page 5, page 6)
Hopf Torus M
Knots on the Cubic Lattice
Hyperbolic knots (3D models added 25 Feb 2003)
Complex knots
Symmetric projections of minimal-stick knots
Interactive knot viewer (randomly chosen knot, requires Java): smooth knots minimal-stick knots equilateral minimal-stick knots crazy knots.
VRML Models
3D Surface Models
Perko pair knots
Moebius strip knots
Stick numbers for minimal stick knots (data only, no pictures)
Knot Diagrams from Dowker Codes
Some excellent references on knot theory.
Some favourite figures from my thesis (PDF and PostScript)
Links to other people's knot sites.

Raytraced Examples

Bizarre (or not-knot-like) Examples

Knotted Sea Things
Various Odd Knots, Unknot Flowers M
Moiré pictures and other weird pictures of things not knots

Other pages

Quote from Clifford Ashley
Interactive Topological Drawing, my thesis
Short discussion on braid theory (incomplete) and a few neat pretzel knots

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

KnotPlot is an OpenGL program that runs on most types of computers. Go to the download site for a free copy.

Related work

Check out these

to see related work by other people.

Author

Robert Scharein,< @cecm.sfu.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

Nick Pippenger
Dale Rolfsen, (Department of Mathematics,U.B.C.)

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, the Pacific Institute for the Mathematical Sciences, and the Centre for Experimental and Constructive Mathematics.

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)

no symbols where none intended