Seamless Mobius Weave

Seamless Möbius Weave (2015)
Hemp twine, two pieces (dyed & natural colors) 3" x 3" x 2"

This summer I studied weaving. I had a delightful time learning from the great Lou Grantham who is owner/operator/instructor at San Francisco Fiber.

After making a handful of traditional pieces in Lou's studio and at home, I then couldn't resist the desire to make a weaving of an unconventional and special topology, the Möbius Strip. But simply weaving a strip and then joining it together at the ends with a single twist in the middle wouldn't do. I wanted it to be seamless, with the warp and the weft running uninterrupted throughout the whole band.

So I needed a special loom, to support the weaving process. My first attempt at loom construction was a single piece of wire, like so:

But this was too flimsy, it wouldn't hold its width. I needed some structural cross-members, so I added the following with careful wire-plier work:

As you can see, each cross-member acts as a bridge to keep the two rails apart at the proper distance, while each bridge remains out of the way of the weaving plane.

From here, the warping of the loom was easy. It consisted of simply wrapping the hemp fiber around the rails and keeping a more or less consistent spacing the whole way round.

Then, the main weaving activity could begin.

But wait!

It is not immediately clear how to go about this. I can't merely start weaving from one edge to the other. Due to the counter-intuitive topology of the Möbius strip, every time you complete a pass around, along one edge, you end up back where you started but along the other edge. (Well, technically, a Möbius strip has only one edge, but if you just look at your local spot on the strip, then you can talk about it having two edges)

So, what can we do about that? Start from the middle and work outwards? With each pass proceeding outwards from the middle along alternating edges?

Consider the following path for the single weft fiber, starting from the middle:

This didn't satisfy me very much, too asymmetric I thought. So I came up with the following alternative:

What I've done is to start the weft in the midline of the strip (indicated by the thick line in the above drawing), as two fibers doubled over and proceeding together. Then the weaving process proceeds symmetrically outwards, with two weft fibers advancing together, each new time around "switching sides" (but not really, because a Möbius strip has only one side, remember?)

I settled on the second, more symmetric option, but was this the right choice? I traded off bilateral symmetry for a double-thickness of warp along the midline. Is this a fair trade? What does bilateral even mean in the context of Möbius topology? Is the lack of obvious symmetry option here related to what happens when you cut a Möbius strip in half?

Back to weaving. In practice, the weaving was more like embroidery, as I was passing the weft through with a needle, over, under, over, under. There is no convenience of heddles to form a shed and pass a shuttle of weft through here. No, each over and under was done manually with needle technique.

Here, you can see the weaving coming along nicely:

Once I was satisfied with the number of weft passes, it was finally time to remove the work from the loom. Only, in this case, the only way to accomplish this is to destroy the loom, turning it into pieces with my wire cutter. In other words, I removed the loom from the weaving!

Once the piece was free from the loom, I noticed it had quite a lot of slack. So I set out to remove the slack, first concentrating all of the warp passes together like so:

And then carefully working the weft through, one bit at a time, until the density gap was closed:

And, finally, I tied the two ends of the weft to the two ends of the warp, to complete the weave, and trimmed the excess down to the knot.

As promised, a seamless Möbius weave.