This is a 12 bight section of a flat braid from Ron Edwards "Advanced Leatherwork - Interesting Braids and Flat Plaits", as created in the Grid Maker from its basic coding of U1 - O3 - U1. He presented it as a flat braid suitable for a belt or hatband.
What we are going to do here is examine the basic structure for some posible cylinderical knots. The basic technique works for any braid structure, but it is probably most productive for the column coded cases, as this one is.
If we drop a vertical line after bight 5, we have a 5 bight X 6 part grid extracted from the original grid.
The run list for 5 bights
from bottom pin 1 to top pin 4
from top pin 4 O1 to bottom pin 2
from bottom pin 2 U1 to top pin 5
from top pin 5 U1 O1 to bottom pin 3
from bottom pin 3 O1 U1 to top pin 1
from top pin 1 U2 O1 to bottom pin 4
from bottom pin 4 O2 U1 to top pin 2
from top pin 2 U3 O1 to bottom pin 5
from bottom pin 5 O3 U1 to top pin 3
from top pin 3 O1 U3 O1 to bottom pin
Now move to bight 7 and repeat the process. Since we changed the ratio between parts (still 6) and bights (now 7) the string run changed, but the structure of the completed knot remained the same. You might notice that now the first full cycle (in red) and the first half of the second are free runs. We don't cross the standing end the first time till we leave top pin 3 at the red arrow.
The run list
from bottom pin 1 to top pin 4
from top pin 4 to bottom pin 7
from bottom pin 7 to top pin 3
from top pin 3 O1 to bottom pin 6
from bottom pin 6 U1 to top pin 2
from top pin 2 O1 U1 to bottom pin 5
from bottom pin 5 U1 O1 to top pin 1
from top pin 1 O1 U2 to bottom pin 4
from bottom pin 4 U1 O2 to top pin 7
from top pin 7 O1 U3 to bottom pin 3
from bottom pin 3 U1 O3 to top pin 6
from top pin 6 O1 U3 O1 to bottom pin 2
from bottom pin 2 U1 O3 U1 to top pin 5
from top pin 5 O1 U3 O1 to bottom pin 1
This one is a little different. With eight bights, we now have a GCD of 2. Of course this means it will take 2 strings for the knot. Otherwise it is similar to the 7 bight, except the bight progression is now 2 instead of 1.
Since I always need to take a closer look at the color patterns of multi-string knots. This one is nicely symetrical, and with 130 or so bights of 1/8th leather will make a novel hatband.
The 9 Bight knot is a three string version (GCD=3). This is the color pattern with two colors. Of course a three color pattern is possible, but I like this one better.
The 10 bight segment is another two string knot and the 11 bight is single string for a total of six knots of increasing circumference derived from one basic braid structure.
This is the algorithm - diagram for the three string knot of 6 parts and 9 bights from above.
The only difference between it and the two string charts we did in Part 1 os the addition of the third section of bightS for the second interweave. The cyclic bight numbers will always have a two space gap and we fill the second with B's to build Interweave 2
One thing you might notice is that 2 is the only bight number over the scan line, so the whole first cycle and the first half of the second are a free run.
