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Two and three pass tile patterns

Two pass tiles

The upper grid to the left is 16 bights of the simplest form of this structure. It is created by cyclic repetition of two diferent sets of string runs. These start at the points marked 1 and 2 at the right bottom corner of the grid.
The code sequence of each is tabulated below the grid.
The first half cycle of the first string run consists of a 2 pass elwmwnt - U2 - the 2 pass element we are centering in parenthesis ( O2 ) - and a single pass element to complete the 5 columns needed for the 6 part structure.
The return sequence for this run (the even half cycle) is, since we have an odd number of code elements is the inverse of the first half cycle.
This process is reversed in the odd half cycle of the second, adjacent string run. The result is to center a diamond shaped set of two pass elements centered between the edges of the braid. The vertical lines across the braid just mark the boundaries from the right edge of the grid for the five specific knots that can be extracted from 16 bights of the braid structure
The second grin is just a rearrangement of the code sequences of the two string runs to tilt the 2 pass elements of the tiles the other way and complete the perceived pattern with the even half cycles of the two string runs.

Since this is a 6 part braid, and we are constrained to bight increments of two to complete both string runs, all knots from these grids will be two string interweaves.
( GCD of 2 ).

In the first grid here we will ad a little trim to the basic pattern. If we take the first structure from the panel above and ad a single over pass to each end of the both string sequences, we get the first grid at the left.All we really did was lock the edges to a single pass at each edge to make the knot easier to dress.

Now in the second grid, we can add a seconf set of tiles in the section in parenthesis. The changes are marked in red.Notice that the extra coding greatly increased the number of specific knots possible it the braid structure.(6 here instead of the 3 in the grid above)The passes underlined in the sequences are the passes that actually form the tiles that we see.

Here is a third set of tiles. There only two possible knots in this the 16 bights of this sequence but the 10 bight one is a nice knot that is almost square.

Some notes

1. So far we have taken a basic central pattern and expanded it into a set of grids that represent 16 descrite specific knots with a common theme in their braid pattern.
2. Each of these knots will have a different "recipe" or run list and each is a two string interweave because of the dreaded GCD rule.
3. Because of the two different string runs involved, these knots ar neither all column coded or row coded. Therefore the run lists, if you use them, will have to be generated manually from a printed grid. ( See working with grids and templates for details of this process. )

Three pass tiles

This is the core coding for a three pass tile pattern, First look at the code sequence of the upward number two pass. The (O3) segment which is the pass that forms the center of the tile is between two equal - U2 - elements.
The number 1 up path is U3-(3)-U1 to place the (O3) part of the tile one column above the center of the pattern and the number 3 up pass of U1-(O3)-U3 places its (O3) tile segment one column below center to produce the diamond shaped tile in the center of the patter.
This is the reason it requires the cyclis repetition of three different string runs for this pattern.

Some trim

This is the core with the single pass elements added in red to lock the edges, with all the possible knots indicated by the vertical lines.
Notice that the third string sequence is not labeled here. That is because none of these six knots require more than two strings to braid, these being the 6 12 18 and 24 bight spans. The 9 and 21 span knots are braided with one string only.
Since this is a ten part braid structure and we are limited to bight increments of three, The GCD between the parts and bights can only be one or two, since three is not a divisor of ten.Of course the 15 bight span is possible, but it would require five strings.

This is the adition of another set of tiles. The extra three pass elements for the second set of tiles raises the part count from the ten parts of the preceding grid to thirteen parts. This results in a structure in which all the knots therein are done with a single string (up to a bight span of 36 bights). This gives a nice small increment fot adjusting the circumference of the knot to fit the work it is going on.

Of course this change alters the three cyclic string runs.They are now-
1-up = O1-U3-(O3-U3)-O1-U1 and 1-down = O1-U1-(O3-U3)-O3-U1.
1 up = O1-U2-(O3-U3)-O1-U1 and 2-down = O1-U1-(O3-U3)-O1-U1.
3 up = O1-U1-(O3-U3)-O3-U1 and 3-down = O1-U2-(O3-U3)-O2-U1.

These are all read left to right as the string is run.They are not of any help in braiding a specific knot, but serve to illustrate the design process for the grid structure.

The two string color pattern

Caveats

Because of their complex form, these knots require some careful planning for a good appearance.
1. The primary thing is that they be sized properly for circumference. If they are not of a circumference that produce an orthogonal crossing of the parts, they tend to produce something I have heard described as "a dogs breakfast". In other words, stay as close to the (1.4 X string width) X Bights circumference as possible for the work. Of course it is easier to adjust the string width and or the number of bights then the size of the work in most cases, but for strap work sometimes a wider or narrower strap will help.
2. When working with leather, anything more than about 3 oz lace should be beveled for a better texture in the knot.
3. Because of space constraints and time limitations, there are no run lists with these knots. If you are not ables to generate them manually from the templates, contact me by the E-mail link on the home page and I will extract any particular one you might want and send it attached to an E-mail.

Credits and references

This work was inspired by a large knot Chris Barr printed in the January APWA journal and helped along greatly by some advice from Mr. Peter Tangey, a member of the same association.
To see an example of the same technique, see Ron Edwards "Advanced Leather Work - Interesting Braids and Flat Plaits",pages 140 - 141, as a 10 strand belt.
In Grant's encyclopedia, the first four figures of plate 180 and the Pampas Button of plate 181 are both variations of the "tile" pattern.