Woven Wedding Rings by Edmund Harriss
I’m happy to present this guest post by my friend Edmund Harris of the Department of Mathematical Sciences at the University of Arkansas. I met Edmund at ACADIA 2011 in Alberta, Canada, and was fascinated by his collaboration with David Celento in creating tiling patterns by projecting higher dimensional objects into lower dimensions. Edmund’s interesting and colorful blog, Maxwell’s Daemon, details his artistic mathematics. This post describes the process of using mathematics and computational design tools to design and fabricate his and his wife’s wedding rings. It is cross posted on his blog.
To design my wedding rings I started with digital and algorithmic systems. Not for any particular reason except that I am good at them and enjoy the sorts of control they both give and take away from me. The computer makes such methods easier and faster, helping to develop the ideas and take them out of my head. Here is my design:
The problem then is how to get the ideas and forms out of the computer. There are several options. For anything two dimensional we now all have incredibly accurate printers at home. Even in 3d pretty great options are starting to emerge, such as those detailed at ShapeWays. Yet these technologies did not feel right for wedding rings, perhaps, in part, because they felt too easy.
Just to make the task harder I also wanted something that retained some sense of the design process; not just a way to make this particular ring but something that could, in principal, just as easily make any of the other rings that I did not choose. In other words, I wanted a process, something that could take in a weave pattern and give out a ring, or in this case, two. This was the point where it was good to have friends and the process detailed in this post was worked out with – and to be honest, mostly by – Eugene Sargent.
Firstly the design shifted a little bit to allow for a casting process and also give a stronger ring.
The next trick was to actually make the woven pattern. We did this using copper wire:
The problem was that we kept on getting lost as we tried to follow the individual strands of wire through the weave. The solution was to consider the crossings not the strands. The strands are labelled 1 to 8, and when they cross they also swap numbers. So if 1 and 2 cross, the strand that was 1 becomes 2 and vice versa. This might sound complicated, but it means that you can forget the individual strands and only need to consider their current position.
In this process we were reinventing the wheel, as it is an ancient technique for creating braids. For example, it is used in the classic hair braiding technique where the hair is divided into three strands. First the right, then the left strand are brought into the middle. With the strands labelled 1, 2 and 3 this would correspond to swapping 1 and 2 and then 2 and 3.
The idea of considering crossings is also used in the mathematical study of braids, called appropriately braid theory. Braid theory can be used to produce images of braids simply by describing the crossings. Using this method we could describe a wide variety of braid patterns and reliably weave them to produce a woven copper ring:
The copper ring can be wrapped round a blank:
We then used epoxy to fill in the overlaps. We used finished blank for sand casting, making the mold:
The mold could have molten silver pored into it:
Here a fairly rough version of the ring is revealed:
With polishing and filing, the cast rings ended up like this:
The key is that this process could be used for any weaving pattern without significant change. In this sense, it is parametric, with the parameter being either a pattern, or more usefully, the abstract listing of the crossings that describes the pattern. On the other hand, the process that uses the parameter is simple handwork combined with the ancient technology of sand-casting. The computer, though a useful tool in the design phase, is not a necessary part of the process.