Parallels and Networks

I noticed an interesting relationship between parallel and network twill threadings a while ago – a parallel repeat is equivalent to redrawing a design line, profile design, or threading on a network with a doubled initial.

To see this relationship, start with a design line or profile design. Here I’ve used a namedraft, generated by using the Fiberworks namedraft generator on the phrase “LindaSchultzWeaving”. The treadling shows the profile design, so turn the draft, then use weave-as-drawn-in to have the profile design in both the threading and treadling.

Make a “parallel repeat” of the profile design. The threading length is doubled and the original four-shaft threading is now eight shafts.

This threading is in parallel form, because it was generated using a parallel repeat, so it hides the initial 2 network. But when “shaft shuffle” is used to move the shafts around and put the threading in “straight” or “twill” form, the initial 2 network becomes obvious.

Other parallel repeat options, like 3-way and 4-way repeats, will respectively triple and quadruple the initial.

These examples all use a divided parallel – each parallel repeat of the threading uses its own set of shafts. The number of shafts needed multiplies with each parallel repeat. What happens if we do an extended parallel repeat, instead?

An extended parallel repeat, rather than adding an extra set of shafts, uses the same set of shafts for each repeat. The fixed interval between each repeat is less than the total number of shafts. And each repeat wraps around the threading when it runs out of shafts to continue in the same direction.

Placing the extended parallel draft in straight form shows the initial 2 network, as well. Or does it?

Something is off in the center, because some of the blocks start on the even shafts, rather than on the odd shafts. Looking more closely, this corresponds to the two areas marked in red, above, where the repeated line wrapped around the threading. In straight form, it shows up as an interruption in the odd-even shaft arrangement.

The same kind of result is shown with a four-way extended parallel repeat. Placing the draft in straight form shows the initial 4 network, with interruptions to the odd-even arrangement corresponding to places where the parallel repeats wrap around the threading.

So both divided and extended parallel repeats show this relationship. Is this useful? After all, it’s easy to use weaving software to “redraw on network”.

Understanding the relationship helps me make sense of how parallel drafts work. I use it in some of my designing with double two-tie four-color double weave. And I use it for some tricks which can be applied to networked and parallel drafts. I will talk about some of these uses in subsequent posts.