I was doing a knot related google image search a while ago when I stumbled on several images that were clearly generated by my software which has come to be called the Advanced Grid Maker in the knotting community. This software started years and years ago when my dad asked me for a visual representation + instructions for tying knots called Turk’s heads. The visual representation is called a knot grid as these kinds of knots can be laid out in a very grid like pattern.
The first version, just called the Grid Maker, was what my dad had asked for. It can walk you through how to tie single stranded Turk’s head knots. It was based on the algorithm diagram laid out by well known knot tyer, Tom Hall, and at the time I implemented it, I hadn’t really tied a Turk’s head before. To test my program, of course, I had to actually tie one. That was my introduction to Turk’s head knots.
As I got more into it, the limitations of the original Grid Maker became obvious. I started thinking about how to represent more complicated Turk’s head knots and decided to implement a way to represent the knot grids that are laid out in several knotting books. I wasn’t well read on Turk’s head knots, but when one of these knot grids was displayed, I could figure out what it meant, it just made sense to me. And so the Advanced Grid Maker was created. I did my best to match terminology with functionality, but I was coming at it from a unique perspective, someone who wasn’t that experienced with knots. I also hadn’t planned on it being used by other people. This made sense to me, and allowed me to tie whatever I wanted, so it only had to make sense to me.
I was surprised, when doing my google search, that I started to see images come up that were generated by my program! I followed the links to see who was using them and to my surprise I came across a site by a French knot tyer, Charles Hamel, who was ripping into the terrible, misleading, ignorant American software that is the grid maker (warning, vulgar language some of which I’ve displayed in his images below as well): http://charles.hamel.free.fr/knots-and-cordages/bats_belfry_17.html. I’m sure something was lost in translation, but the tone of the post was clear, he did not approve of the grid maker. As I read through his post, I had mixed feelings. On one side he’s insulting me, but he also decided to take enough time to tear it a part. I got a kick out of the fact that someone would have such strong feelings about it. It seemed strange until I saw that he had his own software, called Ariane, which also explains how to tie Turk’s head knots, but his software costs money. So for the most part I’ll chalk up his rant to the fact that he’s pushing his own agenda, but let’s break down some of his points. Before I get into the nitty gritty details, I want to stress that we’ll be getting into technical knot talk and if you want to entirely skip it all below here’s the gist:
1) The Advanced Grid Maker is free to use.
2) It can provide instructions for any knot that Ariane can, though it might take more or less work to get it (though again, its free software).
3) The Advanced Grid Maker isn’t your mom, so it doesn’t necessarily take care of you. It can create knots that aren’t standard, and you have to be careful that that’s what you want (or that it’s not).
4) If you know what you’re doing, you can do a lot with the Advanced Grid Maker. There are many knot tyers using it who are very willing to explain how to achieve a certain kind of knot with it. Take a look at the KHWW or the mighty turkshead knot Facebook groups to meet some of them.
5) Feel free to contact me with questions about it any time. I’ll always do my best to answer your question without making you feel ignorant or stupid.
Nitty Gritty Details
Alright, let’s dig in. First, his post is a couple years old, so I’m definitely late to the game. But in my defense, I had no idea about it until relatively recently. Let’s just start at the beginning. Here’s the first grid that he takes a significant amount time and effort to tear apart (he pieces together images to show just how well things don’t line up and everything), when I would have immediately chalked it up to user error. Yes, the Advanced Grid Maker allows you to create a knot like this, but you probably don’t want to tie this knot.
One of the most important features about a Turk’s head is that each strand in a Turk’s head returns to the beginning to form a closed loop (which means it fills the mathematical definition of a knot, in addition to the practical definition). This grid has dangling ends, so its likely not what the user wanted to tie. The grid maker doesn’t enforce grid sizes (though it may in the future) nor does it enforce that strands must return to the beginning. I designed the grid maker to be as flexible as possible, which means the grid can be any number of rows and any number of columns. The one constraint that I do enforce is that the number of columns must be even to ensure that the columns can wrap (another important feature of Turk’s heads, is they are cylindrical in nature, though this rule is broken with flat mats, so I may release that constraint at some point). So as you go from left to right (or right to left) over an edge, you continue to wrap around to the other edge and the knot keeps going. When you start nesting bights, certain multiples of columns are required to make the knot resolve correctly. In the case above, the user probably wanted a knot like this:
All I changed about this knot was I added an extra 2 columns by dragging the right edge out one notch. This allowed the knot to complete correctly and results in a single stranded knot with 3 nested bights using an over 3 under 3 column coding. Which brings me to Hamel’s point about nomenclature. He seems to think his way of describing knots is the end all be all way to describe them, citing Schaake and Turner. He also says that the grid maker is complete junk because of how it describes a knot. Well, I can’t say I’ve read much Schaake and Turner, and I’m sure they’re smart guys who know their knots, but the grid maker strives to be as flexible as possible to allow for many different kinds of knots which probably results in naming problems. My naming scheme is simple, if I used a feature to achieve a certain kind of knot, then I probably named it after that knot. For example, the Pineapple Grid, fills the grid with nested bights as you would want when tying a pineapple knot. Of course, this doesn’t always result in a standard pineapple knot (which to be honest, I’m not exactly sure what the standard is). It can be used to tie single stranded or multistranded nested bight knots with strands that don’t necessarily line up the standard way and I did that intentionally to allow for flexibility. I probably should have just named it nested bights, to avoid the wrath of Hamel. All of the grid settings behave like that. They fill the grid with some kind of pattern, so when you resize the grid (generally by dragging the corner so you can see the changes in real time), it fills in the grid. Take the Hansen grid, for example, a Hansen knot is named so because of how the knot is generally tied, by doubling a standard Turk’s head and splitting the pairs with another strand (a technique described by Hansen). It results in the bights looking a certain way, which is two nested bights next to a single bight repeated all the way across. The grid maker does just that, it repeats that pattern on the top and bottom, but given a certain number of rows and columns it’s not necessarily a standard Hansen knot. Again, this is to allow for and encourage flexibility and experimentation with a certain kind of look rather than a certain naming scheme.
To show just how flexible to the grid maker is, here is a knot that has nothing to do with Turk’s heads, the bowline. It will give you instructions for tying it and everything! I’ll admit that I haven’t used Ariane, but I’ll bet it can’t tell you how to tie a bowline (though I could certainly be wrong).
Given how flexible the Grid Maker is, how would you name how many parts and bights the bowline has? Well, the Grid Maker does its best to tell you. It simply counts the bights, regardless of where it is in the knot and divides by 2. In standard Turk’s heads that works out just about right as you usually specify how many bights are on the top or bottom (which just about always match). The number of parts is calculated by how many times the knot completes a full loop across the grid. In the case of the bowline, it’s 1 part x 5 bights, which doesn’t really mean anything. At the time of Hamel’s post, I think the parts and bights were simply calculated by the number of rows and columns which can easily be calculated for standard Turk’s heads knots, but doesn’t hold water when switching to Pineapple or other knots which is a major source of criticism by Hamel. Oh, well! Hopefully, it holds up a little better now. The grid maker also had issues with calculating facets vs crossings, which all should be correct now. Hamel really laid into me for that one!
Let’s keep going with Hamel’s examples. Here’s the next grid that he calls out (I left the file names as he named them, in this case ALLHK-secondshit.jpg, I don’t think he thinks too highly of it):
Now this grid actually is a knot of the Turk’s head-like persuasion, he just doesn’t think too highly of it for a couple reasons. One, it uses an over 4 under 4 column coded weave pattern (the coding). Since it was described as being a Pineapple Knot, he thinks it should be an over 2 under 2 column coded weave pattern (a 2 pass knot). That’s something I completely disagree with, and one of the reasons I implemented the Grid Maker the way I did: you can do what you want. If you tied this knot it would look like a 4 pass pineapple knot, when in reality its 2 stranded! Who cares if it doesn’t technically line up with the standard naming scheme? The other problem he calls out (which I agree with), is the pattern doesn’t match up quite right on the left and right. In this case, once completed the knot would have a section with an over 8 because of how the number of columns relates to the over 4 under 4 pattern. Because I fill the grid with the pattern as best I can and in this case the last few columns are only able to accept half the original pattern, when it repeats as it changes edges, the pattern is off a little bit. Hamel actually does an excellent job illustrating this in this image (this one is named ALLKHSHIT.jpg, really??):
Notice how on the left and right the pattern doesn’t follow the right of the knot. I can simply shift the pattern over to illustrate the problem when the issue isn’t on the seam of the image.
Or for those who aren’t as savvy with grids, here it is in 3D:
I probably posted this knot as an early test of the grid maker. I think he even points that out for me. Yep, he does (notice the thread title, A test PK).
That’s not to say there is anything wrong with the above grid as Hamel would have you believe. There are a few quirks which may or may not change how you think about the knot. The simple fix is to adjust the number of columns to either 4 more or 4 less, which could lead to a change in the number of strands. You could shift the bottom bights of the knot, which may also change the number of strands or how the strands are laid out (notice how at the top the white strand is the inner bight, but at the bottom its the outer bight, shifting the bights can shift that layout). This is the type of workflow you have with the grid maker, which may be different than your traditional way of designing knots and is certainly different than how Hamel would say is “correct”, but there is nothing wrong with the above knot.
On to the next example (though, its just more of the same). Here is the next knot Hamel takes issue with:
Again, he picks out minute details about the knot, when in reality there’s nothing wrong with the knot, it’s just different than the closest “ideal” knot he chose to show with Ariane (which I assure you the Grid Maker can tie as well, as you’ll see). Looking at this image, I actually like it the look of the knot, along with the color scheme. Which brings up another goal of the Grid Maker, to give a good visual indication as to what the knot would look like. I think whoever made this knot, chose a good color scheme as well Let’s talk about what Hamel has to say about it, though. He insists that this is NOT a 3-pass knot, but instead a combination of 1-pass, 2-pass and 3-pass. He may be correct, but frankly, who cares? At first glance anyone with a little experience with these knots would call this a 3-pass herringbone. It’s when you get into the minute details that you can see a couple issues that Hamel so aggressively calls out.
He specifically calls out the O1, O2 and O3 near the top calling it a combination of 1-pass, 2-pass and 3-pass, which is absurd. The coding just like most things in Turk’s heads is cyclical. All he did was offset the coding a bit to make it how he wanted it to look (which may be some kind of standard knot). I’ve marked up his ideal knot to similarly show how he was breaking down the other knot. My dots are pointing out the U1, U2 and U3 of his knot, which is a result of just shifting the coding a bit.
Lastly, he does point out that it’s not a Type 1 Pineapple Knot because the 3 strands aren’t entirely nested within each other. The outer knot is correct how a Type 1 Pineapple knot would be laid out, but the inner two strands are actually made up of a Type 2 Pineapple Knot because each knot’s bight boundary extends down the same distance (rather than one within the other for a Type 1). Who cares? Here is his “ideal” single stranded knot using the grid maker, which of course illustrates how you’d lose the 3 color scheme as it’s all now 1 strand! I’ll leave it to you to decide which one is better. Though I’ll give you a hint, it’s up to you to decide what knot is for what purpose.
And that’s about it. I hope you see what Hamel’s post really is, a rant meant to get you to buy his software rather than using a competing free alternative. He ended his post with a few knots to show off Ariane, so I’ve included the same knots rendered with the Grid Maker, along with run lists and 3D renders of them. If anyone needs help with how to interpret these grids/instructions, let me know. Enjoy!
Strand 1 From A1 to J4 From J4 O1 to B2 From B2 U1 to K5 From K5 U1 O1 to C3 From C3 O1U1 to L1 From L1 U2 O1 to D4 From D4 U2 to G1 From G1 U1 O1 to E3 From E3 U2 to H5 From H5 U2 O1 to F2 From F2 U1 O2 to I4 From I4 U1 O1U3 to A2 From A2 O3U1 O1 to J5 From J5 U1 O3U1 O1 to B3 From B3 O3U2 O1 to K1 From K1 U1 O1U2 O1U1 O1 to C4 From C4 O4U3 O1 to L2 From L2 U2 O1U1 O2U1 O2 to D5 From D5 O3U2 O1U2 to G2 From G2 O1U1 O1U2 O2 to E4 From E4 U3 O1U2 to H1 From H1 U2 O1U1 O2 to F3 From F3 U1 O3U2 to I5 From I5 O1U1 O1U3 O3U1 to A3 From A3 O1U1 O2U1 O1U2 O1U1 to J1 From J1 U1 O3U1 O4U1 O1 to B4 From B4 O1U1 O1U1 O3U3 O1U1 to K2 From K2 U4 O2U3 O2U1 O1 to C5 From C5 O2U1 O2U2 O2U4 O1 to L3 From L3 U1 O2U3 O2U1 O3U1 O2 to D1 From D1 U1 O4U2 O1U3 O1U2 to G3 From G3 O1U1 O2U2 O2U2 O3 to E5 From E5 U1 O1U1 O1U3 O2U2 O1 to H2 From H2 U2 O4U2 O3 to F4 From F4 U1 O3U5 O1 to I1 From I1 O1U1 O1U3 O5U2 O1U1 to A4 From A4 O1U1 O2U4 O2U3 O1U1 O1 to J2 From J2 U1 O1U1 O1U1 O3U2 O3U1 O1U1 O1 to B5 From B5 O1U1 O1U2 O2U2 O3U4 O1U1 to K3 From K3 O1U4 O2U2 O3U3 O2U1 O1 to C1 From C1 O1U2 O3U2 O2U3 O2U4 O1 to L4 From L4 O1U1 O1U1 O2U3 O3U1 O3U1 O3 to D2 From D2 U1 O1U2 O3U3 O1U3 O1U2 to G4 From G4 O2U2 O3U2 O3U2 O3 to E1 From E1 O1U2 O2U2 O2U3 O3U2 O1 to H3 From H3 U1 O2U1 O3U1 O3U3 O3 to F5 From F5 U1 O2U2 O1U3 O2U3 O1U1 to I2 From I2 O1U1 O1U2 O2U1 O3U2 O3U1 O1U1 O1U1 to A5 From A5 O1U1 O1U2 O1U3 O1U3 O3U3 O1U1 O1 to J3 From J3 U2 O2U2 O2U2 O3U3 O3U1 O1U1 O1 to B1 From B1 U1 O2U2 O2U3 O2U3 O3U4 O1U1 to K4 From K4 U1 O1U1 O2U3 O3U2 O3U3 O2U1 O1U1 to C2 From C2 O1U1 O1U2 O3U3 O2U3 O2U4 O1U1 O1 to L5 From L5 U1 O1U1 O1U1 O3U3 O3U1 O3U3 O2U1 O1 to D3 From D3 U1 O1U3 O3U3 O1U3 O2U3 to G5 From G5 O3U3 O3U2 O3U2 O3U1 to E2 From E2 O1U3 O3U3 O2U3 O3U2 O1 to H4 From H4 U1 O3U3 O3U2 O3U3 O3 to F1 From F1 U3 O3U3 O2U3 O3U3 O1U1 to I3 From I3 O1U1 O3U3 O3U2 O3U3 O3U1 O1U1 O1U1 to A1
Strand 1 From A1 to F5 From F5 O1 to B5 From B5 U1 to D3 From D3 O2U1 to C2 From C2 U2 to E5 From E5 O1U1 O1 to A5 From A5 U2 O2 to F4 From F4 O2U1 O1U2 to B4 From B4 U2 O1U1 O2 to D2 From D2 O2U2 O1U2 to C1 From C1 U2 O2U1 O1 to E4 From E4 U1 O2U2 O2U1 to A4 From A4 U1 O1U1 O1U1 O2U1 O1 to F3 From F3 O2U3 O2U2 O2 to B3 From B3 U2 O3U2 O2U2 to D1 From D1 O2U3 O3U2 to C5 From C5 U1 O1U1 O2U3 O1 to E3 From E3 U1 O2U1 O1U2 O3U2 O1 to A3 From A3 U1 O2U2 O1U2 O2U2 O2 to F2 From F2 O3U2 O2U1 O2U3 O2U1 to B2 From B2 U2 O2U2 O1U2 O3U2 to D5 From D5 O2U3 O3U2 O1U2 to C4 From C4 U3 O1U2 O2U3 O3 to E2 From E2 U1 O3U2 O2U2 O3U3 O2 to A2 From A2 U1 O2U3 O2U2 O3U2 O3U1 to F1 From F1 O3U3 O2U3 O2U3 O3U1 to B1 From B1 U2 O3U2 O3U2 O3U3 to D4 From D4 U2 O2U3 O3U3 O3U2 to C3 From C3 U3 O3U2 O3U3 O3U2 to E1 From E1 U1 O3U3 O3U3 O3U3 O3 to A1
Strand 1 From A1 to E8 From E8 O1 to B7 From B7 U1 to F5 From F5 O2U1 to C4 From C4 U2 O1 to D1 From D1 O1U1 O1U1 to A9 From A9 U1 O1U1 O1 to E7 From E7 O2U1 O1U2 to B6 From B6 U2 O1U1 O2 to F4 From F4 O2U2 O1U2 O1 to C3 From C3 U2 O2U1 O2U1 to D9 From D9 O2U2 O2U2 O1 to A8 From A8 U2 O2U2 O2U1 to E6 From E6 O1U1 O1U2 O2U1 O1U1 O1 to B5 From B5 U1 O1U1 O2U2 O1U1 O1U1 to F3 From F3 O1U1 O1U1 O1U1 O2U1 O1U1 O1U1 to C2 From C2 U1 O1U1 O1U1 O1U2 O1U1 O1U1 to D8 From D8 O1U1 O1U1 O1U1 O1U1 O1U1 O1U1 O1 to A7 From A7 U1 O1U1 O1U1 O1U2 O2U1 O1U1 to E5 From E5 O1U1 O2U1 O1U1 O1U1 O1U1 O1U2 O1 to B4 From B4 U1 O1U2 O1U1 O1U2 O2U1 O2U1 O1 to F2 From F2 O1U1 O2U1 O1U2 O1U1 O1U1 O1U2 O1U1 to C1 From C1 U1 O1U2 O1U1 O2U1 O1U1 O1U1 O2U1 to D7 From D7 U1 O1U1 O2U1 O1U2 O1U1 O2U1 O1U2 O1 to A6 From A6 U1 O2U2 O1U1 O2U2 O2U2 O2U1 to E4 From E4 U1 O1U1 O2U2 O1U2 O1U1 O2U1 O1U2 O2 to B3 From B3 U1 O2U2 O2U1 O2U2 O2U2 O2U2 O1 to F1 From F1 O1U1 O2U2 O1U2 O2U1 O2U1 O1U2 O2U1 to C9 From C9 U1 O1U2 O2U1 O2U2 O1U2 O1U1 O2U2 to D6 From D6 U1 O2U1 O2U2 O1U2 O2U1 O2U2 O1U2 O2 to A5 From A5 U1 O2U2 O1U1 O1U1 O2U3 O2U2 O2U1 O1U1 to E3 From E3 U1 O2U1 O2U2 O2U2 O2U1 O2U2 O1U2 O2U1 to B2 From B2 U1 O2U3 O2U2 O1U1 O1U2 O2U2 O3U2 O2 to F9 From F9 O2U1 O2U2 O2U2 O2U2 O2U2 O1U2 O2U2 to C8 From C8 U2 O1U2 O2U2 O2U2 O2U2 O2U1 O2U2 to D5 From D5 U1 O2U2 O2U2 O2U2 O2U2 O2U2 O2U2 O2 to A4 From A4 U1 O2U2 O2U2 O1U1 O2U3 O3U2 O2U2 O2U1 to E2 From E2 U1 O2U2 O2U2 O2U3 O2U2 O2U2 O2U2 O2U1 to B1 From B1 U1 O2U3 O3U2 O2U1 O2U2 O2U2 O3U3 O2 to F8 From F8 O2U2 O2U2 O2U3 O2U2 O3U2 O2U2 O2U2 to C7 From C7 U2 O2U2 O2U2 O3U2 O2U3 O2U2 O2U2 to D4 From D4 U2 O2U2 O3U2 O2U3 O2U2 O3U2 O2U3 O2 to A3 From A3 U1 O3U2 O2U3 O2U1 O2U3 O3U3 O2U2 O3U1 to E1 From E1 U1 O2U2 O3U2 O2U3 O3U2 O3U2 O2U3 O2U1 to B9 From B9 U1 O2U3 O3U3 O2U2 O2U3 O2U2 O3U3 O3 to F7 From F7 O3U2 O3U2 O2U3 O3U2 O3U3 O2U3 O2U2 to C6 From C6 U3 O2U3 O2U2 O3U3 O2U3 O3U2 O3U2 to D3 From D3 U2 O3U2 O3U3 O2U3 O3U2 O3U3 O2U3 O3 to A2 From A2 U1 O3U3 O2U3 O3U2 O2U3 O3U3 O3U2 O3U2 to E9 From E9 U1 O3U2 O3U3 O2U3 O3U3 O3U3 O2U3 O3U1 to B8 From B8 U2 O2U3 O3U3 O3U2 O3U3 O3U2 O3U3 O3U1 to F6 From F6 O3U3 O3U3 O2U3 O3U3 O3U3 O3U3 O3U2 to C5 From C5 U3 O3U3 O3U2 O3U3 O3U3 O3U3 O3U3 to D2 From D2 U2 O3U3 O3U3 O3U3 O3U3 O3U3 O3U3 O3 to A1
I don’t think this one would hold together so well. It’s a facet count test, though, so I wouldn’t want to take anything out of context…
Strand 1 (peru) From A1 to D3 From D3 to C4 From C4 to E8 From E8 O1 to B1 From B1 U1 to E5 From E5 U1 to C5 From C5 U1 to D1 From D1 O1U1 to A2 From A2 U2 to D4 From D4 U1 O1 to C6 From C6 O2 to E2 From E2 O2U1 to B3 From B3 O3 to E7 From E7 U1 O1U1 to C1 From C1 O1U2 to D2 From D2 U1 O3 to A3 From A3 U1 O1U1 to D6 From D6 U1 O2 to C2 From C2 U1 O2U1 to E4 From E4 U1 O3U1 to B4 From B4 O1U1 O3 to E1 From E1 U2 O3 to B2 From B2 O5 to E6 From E6 U2 O1U1 O1U1 to B5 From B5 U1 O1U1 O1U1 O1 to E3 From E3 U1 O1U1 O3 to C3 From C3 O5 to D5 From D5 O1U3 O1U1 to A1