Triskeles, topology, and Celtic knots

Hey everyone. I have so much missed being in the smithy doing all that metal magic stuff. I really feel amazed by metalsmithing, even after , ohhh, 25 years! The things it does!!!
John and I have been playing with Celtic knot ideas. He is so brilliant..always coming up with new ideas to try out!

Today we are musing on triskeles, topology, and Celtic knots. A triskele is a Celtic design of a triple spiral. Which means three spirals. The spirals must all go in the same direction. Clockwise or counter clockwise. (Or sun-wise and counter sun-wise.) I feel intuitively that these spirals have to do with time and the progression of things, but thats just me musing.


My 'magic method' of Celtic knot construction uses paper folding & cutting to create symetries of interlocking pattern. I invented this method in '86 while playing with kirigami, a Japanese paper folding & cutting method.

Since a triskele is a-symetrical in that it goes around only in one direction on its spirals, it cannot be made by folding & cutting. However, one can take a circle of paper, slit it, and fold that piece into equal thirds. If you draw a spiral on that and cut it out then one of the three resulting spirals will face the wrong direction.


OK. Here is that design.

See how the two right sprials face

other. Not good.

Next thing I did was do the same sort of slit & fold circle BUT then I cut the folds away so they are, in essence, just three stacked fan-shaped pieces of paper. These I drew a spiral on & cut out carefully. When I had done that I laid them out. One still faced the same way as another, but now I just was able to flip that one over to make them all go in tha same direction. I hear you saying "So what?" Well so you can use this method to design very pleasing triskeles. Like this one I just did

Yes, I cut off a wee bit on one side.

But it is a nice symetry, eh?

I have been doing other knots too. I cut a trilaterally (three sided) symetrical one a few days ago. Traced it on to paper, scanned it in, and then bucket-filled the backround blue behind it. Doing this one needs to only make sure that all the 'cells' of the design are closed so the color does not run over. Go ahead and take it to your photo-art program and play with it! Color, distort, have fun.

I am going to do a tutorial on the basic knot method on youtube and/or google soon. Keep your eyes open & google me!

OK, I also did a quick pentalateral (star shaped) knot this morning, and hand drew five separate triskeles in to it after I was done making the design. Here is that. Its hard to see the triskeles on the five end things, but they are there. I like the star formed in the middle...

As you can tell by the uneven nature of the paths of this knot, I cut it out of paper. I drew the little 'over and under' lines which make it a Celtic interlacing pattern, in fact a two dimensional representation of a three demensional design. OK? Then when done I hand drew the triskeles in. But they do not look nearly as nice as the ones above that I cut out! Cutting stuff out gives you a crisp sort of symetry. Plus its sort of magic, you know?
I have nattered enough for the nonce. My brain is going in spirals.