Celtic style knots and braids

My interest in knots and braids was recently rekindled when I started building a harp and wanted to decorate it.

Long braids

For this I started using the design method described on Marc and Shelly Wallace's knot pages but unfortunately it quickly showed itself to be too limited, since it only allows for square and rectangular knots. These are ok for simple decorations as well as for building blocks for long braids such as the one shown here, but the method is essentially useless for filling out more complex shapes.

Instead I now use a method devised by the french mathematician Christian Mercat. This method is far better for designing decorations, as one of its features in the concept of a encapsulating graph, which clearly defines the shape of the finished knot.

Shapefilling knots

In this method I start with the area available, filling it out with a nicely symmetric grid. The picture on the right shows the right side of the grid marked out a bit more visibly, with its complement graph in red.

I've found that once you've designed the graph for the knot, Steve Abbott's Knots3D program is excellent for the phase where you modify the knots crossings for added effect, because you can see the results immediately, including whether you accidentally (or by design) made a disjoint knot.

Unfortunately, it isn't quite good enough yet to make the finished knot but it is definitely enough to avoid making a monster such as the one to the right.

You'll notice that for the finished knot, I simplified the upper corners, mainly because when I was bulking up the knot I could see a problem with getting room enough to work in.

Swirly initial letters

These are easy to get fascinated by once you start looking for knots in places such as the Book of Kells.

ere is one I made by mixing parts of a "B" and "H" from The Book of Kells because I wanted something to put on my coffee mugs.

I changed a couple of details from the original letters. The lower knot had a fault that caused it to not be singularly connected and in a continuation of an old tradition, I used a self portrait instead of the original head.