Celtic Knotwork: the ultimate tutorial

1. Introduction

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You might be interested in celtic knotwork because you saw an illuminated page of a medieval Bible such as the Book of Kells, which can be found at the Trinity College in Dublin.

You may like to try and do similar things such as this page I illuminated for an article I wrote in Pour la Science, the French version of Scientific American. Calligraphy by Chantale Fachinetti.

Or you’d like to have a tatoo but unfortunately the guy down the street is not as talented as Pat Fish who does very nice things such as the image on the right.

streetmathYou can even draw on the pavement, the #StreetMath way.

In Ireland you can stumble against stones which prove that these patterns are not only the last trendy stuff.

But knots and links have been around for quite a while.

And if Europeans call them Celtic, the people from India know them for longer (see ISKFA06) and the Islamic world boasts techniques much more elaborate than the Celts. Visit Craig Kaplan website for a wonderful java program on Islamic tiling and interlacing.


In this tutorial, you are going to learn, in less than one hour, how to draw such designs. The technique is summarized in the following picture.

A graph (in red) codes a knot, to construct it, you place little crossings on the middle of each edge. Then a simple maze-like procedure allows you to join these little bits of threads into continuous lines that you can smooth. After that, you draw the over/under pattern, using an easy guide. Finally you inflate your knot, like a road in which the previous threads are the yellow line on the middle of the road. And you’re done, it’s that easy! Please note that I am not concerned here with other celtic designs. You may find excellent books on these, for example the one wrote by the great artist Aidan Meehan.

Cari Buziak treats this sort of things too, as well as mastering knotwork.

In fact, it is so easy that a computer can do that, there are several implementations of my methods. The best ones are KnotPlot, KnotScape, Steven Abbott and the magnificent KnotsBag.

This tutorial stems from two series of courses in illumination techniques I gave in the calligraphy school of the Alcuin Institute at St Cyr sur Loire in 1994 and 1996. I thank Richard Forestier, Chantale Facchinetti and Agnès-Frédérique Forestier for having the grace and patience to welcome me. Without their care and interest in the subject and their passion for things well made, I would never have prepared this tutorial and it was thanks to them that I worked out ways to describe intelligibly the mathematical objects (very simple for a mathematician) that form the basis of the theory. I thank them here.

The course really begins from the basics up.

2 Forum messages

  • the FORMA commurative issue related this topic 5 December 2007 11:15, by Nagata shojiro

    Dear sirs

    I am glad to contact with you as a researcher interested in Celtic knot and other traditional string cycle patterns.

    It has Just passed one year since the time when we had held the
    international symposium on katachi/form in folk/traditional arts(ISKFA06 Japan)
    After a long time, we now published the commemorative issue of the journal
    (English version) FORMA and now uploaded all texts of it to the free web
    of one of the co-organizations Society for Science on Form, Japan
    http://wwwsoc.nii.ac.jp/form/index.html (sorry mostly in Japanese)

    The figure of the cover page is Kolam image calld as Diamond
    Carpet and the four color traces show that the original pattern looks like
    in Chaos, however consists clearly of the structure of Swastika with
    rotating symmetry, and the web image display the animation of that tracing.

    I am considering to send you to a copy(s for co-authors) of a printed matter
    of the Journal with surface/air mail.

    Please give me your any comments or opinion about it.

    produced by me, show some movies introducing how to draw Kolam in India with
    real performances

    Thanks again
    with best regards
    Nagata shojiro (KASF) the editor in chief of this issue

    PS Appreciate to inform this news in your web or to your related persons

    Reply to this message

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Thursday 17 August 2006, by Christian Mercat

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