5. Twist

5.1. Transformations. As tilings can be used to generate weaving patterns, also weaving patterns themselves can be used to generate other weaving patterns. We will discuss and illustrate some of the possible transformations that can be used to generate new weaving patterns and also new weaving structures.
5.2. From Lines to Closed Loops. In a plain weave there are straight crossings between the lines. You can say that each line at each crossing point takes the second exit. If we change that, so instead of the taking the second exit we take the third and we do that with both lines of the crossing, we will get a twist at the crossing point of our weaving. The first twist (Figure 21a) will just cause a defect in the weaving. But applying this twist on every crossing point in the weaving will transform our line weaving into a weaving with closed loops (Figure 21c). Figure 22 shows the result of this transformation starting with the three way weave.
Figure 21a: One defect
Figure 21b: One loop
Figure 21c: Loop weaving
Figure 22: Three way
5.3. Change of Rhythm. The next operation can be seen as a change of rhythm: instead of over-under-over-under (notation: 1-1) we will change to over-over-under-under (notation: 2-2). To achieve this we just change some of the crossings from over-under to under-over. In Figure 23 you can see the result of this operation applied on the weaving of Figure 21c.
Figure 23: Rhythm 2-2
Figure 24a: Rhythm 3-3
Figure 24b: Rhythm 4-4
Figure 24c: Surface