Knot Mosaic Space

Knot Mosaic Space is an online repository for information related to knot mosaics. The concept of a knot mosaic was first introduced by Sam Lomonaco and Louis Kauffman in 2008. The idea is to create the image of a knot or link on a square grid using any number of tiles chosen from the collection of 11 tiles pictured here.

Available Tiles:

Here are a few examples of knot mosaics.
 

For a complete introduction to knot mosaics, users are encouraged to explore the various works cited on the references page. This website features a complete table of knot mosaics for prime knots with crossing number 10 or less. Additionally, knots with crossing number greater than 10 are included if a mosaic has been found. Users are also encouraged to create their own knot mosaics using the Knot Mosaic Maker.

Links

Table of Knot Mosaics - Updated as new results are found. Knot Mosaic Maker - Interactive tool for creating and identifying knot mosaics. Link to Source Files - Provides access to the source code of the pipeline search algorithm. References Older table of Knot Mosaics (not being updated)

More Examples

Knot Mosaic Space was created by Aaron Heap and his students at SUNY Geneseo and is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.