This is a blank work sheet to create a running list for any knot up to 10 bights and 16 parts. We will go through it step by step to create such a list.
When we depart from the simple casa coding of a column coded knot such as the basic turkshead, we need a tool to determine the braiding sequence wrap by wrap. My preference is what I have called a running list. This is a tabulation of the crossings by the running end for each trip across the knot in the order we make them up and down from start to finish. This material is an adaption of the algorithm diagram from Tom Hall's book "Introduction To Turkshead Knots" to create these lists with the least effort. I worked this out to use with the "mixed code" knots that I couldn't count the code into as I braided them. It works fine for regular "casa" coding but I used a different coding in the first two examples to make the point that it is independent of coding.
What this method allows you to do is design unique knots of any size and code pattern easily.
This diagram scans the knot as if it was oriented horizontally. My habitual use of a vertical orientation of the knot cylinder makes the columns seem to run horizontal in the templates and sketches instead of vertical as common usage of the term column would indicate. As this is just another matter of perspective, it should'nt cause a problem so long as you keep it in mind.
This is a blank work sheet to create a running list for any knot up to 10 bights and 16 parts. We will go through it step by step to create such a list.
The first step is to evaluate the knot definition with the Parts/Bights=the whole number N + the remainder R (P/B=N+R).Then get the value of V from V=B-R. The value of V is actually the CCW bight progression. The B count is just the number of Bights in sequence. This gives the numbers we need to build the scan chart.
Now for the length of the bight count we place the bight numbers in the B prog. line in intervals of V (3 in this case). (What we are doing here is going around the knot in a CCW direction and marking the start of each wrap in order). We will build the scan chart from this and the coding sequence of our choice.
Now we construct the scan line from the B prog. above it. We start with the second number and enter the B prog. numbers in the scan line in sequence to the length of the code sequence. As the code sequence is always one less than the number of parts, we use 8 for this 9 part knot. As with the B prog line, when we get to the end of the sequence we loop back to the start and continue.
The last step here is to enter the coding pattern we want. The one I have chosen for this example is a 1-2-1-1-2-1
for a conventional coding perspective of the knot. I have found the best practice is to use a symetric pattern for ascetic reasons but it is not absolutely necessary.
Now we can fill the Running List from the scan chart.We will need only the segment outlined in red. Here is the labor saving part. We only need to work with the second half of each wrap (the ones with the down arrow in the list). Look for each wrap number in the scan line and enter its code in the down arrow row of the list in the code column indicated.
To finish up just look at each column for the first appearance of an O or U and fill the rest of the column downward with the same code.
This is just for knots with an odd number of parts, we will get to those with an even number of parts shortly.
We can do this because in all odd part knots the first half wrap (going up) is a duplicate of the previous half wrap (coming down) in every wrap.
Notice that the second half of wrap 4 is in fact the code sequence we started with in the code line of the scan chart.
This is a wrap by wrap braiding on a 4 bight mandrel using the regular bight increments. In looking at these remember that the new wraps (in green) don't cross themselve going up, only coming back down.
When it is tightened up it has the pattern to the left.
This is a list for an 8 part X 5 bight knot constructed as the one above. At this point there is nothing different from the odd part knot before.
You may notice that I used the braid entry and exit convention for the second half of a wrap in choosing the code scheme. This was to give a conventional coding perspective to the knot. If I had begun and ended it with an under the resulting list would been for a "sobre" knot.
It is in finishing the columns that the even part differs.
Instead of just repeating the first over or under beneath the first appearance of the Xing in each column to the bottom, we start with it and alternate the pattern down. (Notice that the result of this is that the replication of the down pass in the next upward pass is a mirror image instead of a duplication.)
The knot done. 
This is a knot in which the number of bights is more than the number of parts. When we try the P/B=N=R on it things seem to go to pot.
The whole number N is 0 and the remainder is a long decimal fraction. What this really tells us is that the running end does not cross the standing end in the first wrap. This makes the CCW bight progression ( V ) equal to the difference between the number of bights and the number of parts.
We need to make the B progression line to the full length of the bight count to get the sequence right but we only use a portion of it in the scan chart. (Note that wrap 1 is left out, indicating that is a free run completely as the 0 in P/B=N+R indicated.)
The run list is done as always.
Copyright Sidney Wood 12/27/07
