Cellular Chainmaille Theory Grains and Grain Transformations

What is a Grain?​

Grain Types​

Grains are easiest to recognize in their continuous forms. A continuous grain is simply a grain that runs the length of the form, uninterrupted. Currently, there are 6 recognized grain types;

• Adjacent​

  Adjacent is the root of grains. Just like you can't have cells without rings, you can't have additional grains without adjacent. By layering, offsetting, and crossing adjacent we find the other grains. Without a cross grain, adjacent is just a row of rings.

• Lean​

  Lean is a grain where each additional ring "leans" on or supports the previous ring. Without a cross grain, lean is just a row of rings. In CCT, lean is designated as the primary grain due to it being a direct translation of a single ring. This means that, in regards to grain transformations, a weave made with 2 lean grains would be the standard form of the weave that all grain transformations develop from

• Step​

  Step is a grain where each additional ring alternates between being above or below the previous ring. Without a cross grain, step is just two offset layered rows of rings.

• Parallel​

  Parallel is a grain that alternates between a central single ring and a split pair of rings (one on either side of the single ring). Without a cross grain, parallel is just three offset layered rows of rings.

• Twist​

  Twist is a grain made up of two adjacent grains (making it, in and of itself a cross grain). Without an additional cross grain, twist is more commonly known as 2 in 1 chain.

• Spiral​

  Spiral is a grain transformation of twist, This is due to each additional ring, instead of alternating like twist, being continuously rotated in the same direction as the previous ring, either positively or negatively. Without a cross grain, spiral is more commonly known as 2 in 1 chain - spiral form.

Minimum Number of Rings​

Not all grains will be continuous. Some may, through segmentation or further modification, be interrupted. With interrupted grains, identification may not be as apparent. In these cases, each grouping of rings will have a minimum number of rings before it can reliably be identified as part of a grain. This is because a grain type is based upon rings positions relative to the position of preceding rings in the grain.

• 1 ring will always be identified as adjacent.
• 2 rings can be identified as either adjacent, lean, or twist
• 3 rings can be identified as either adjacent, lean, step, parallel, twist, or spiral

Please Note: In most cases, with anything CCT related, I generally stop at a maximum of 3 instances. This is because of what I affectionately call "The Rule of 3's" (if I ever have time to extensively test it, I'll write an article about it). Suffice it to say, that after 3 instances, things can be broken down into multiplications of previous elements, the crossover point being 6. Anyway, back to ring minimums.

Crossing Grains - Chain Forms​

The number of grains present and how they are connected to each other can give a rough approximation of what chain form is being looked at.

• 2 Grains - Cross Grain Chain (this is the base of other chain forms)
• 3 Grains - 3/4 Chain
• 4 Grains - Tube

3/4 Chain​

When adding a third grain to a cross grain chain (i.e. faceted modification) to create a 3/4 chain, it is generally done in a way that results in what is called a "Paired Grain." When a grain is paired, it means that the pair is treated as a single element. Break the pair and what is left is a different "weave."

Side Note: I have weave in quotation marks because while most 3/4 chains are listed as different weaves, CCT sees them as the same weave in different forms. (i.e. Half Persian 3 in 1 is a cross grain chain, Three Quarters Persian is a 3/4 chain and Full Persian 6 in 1 is a tube chain.)

Pairing of grains come in three varieties (two are confirmed):

• Layered - A direct translation of the grain being paired, with the same connections as the original.
  
• Mirror - A direct translation of the grain being paired that is a mirror image of the original, with the same connections as the original.
  
• Staggered - Staggered has had limited research done as a paired grain type. Currently, only lean grains have been looked at and only in relation to inversion locks. Under those conditions it is a pair of layered leans done in the same direction (clockwise or counter-clockwise) from diagonally situated "pivot points" in the same cell. It is very hard to see without the cross grain being present. As a whole, "staggered" is very much still under investigation.
  

Parallel Note: You may have noticed that parallel grain is not present in the above section. There are two reasons for this:

1. Parallel is symmetrical, if you layer or mirror it, you get the same result.
2. 6 adjacent layers requires a really large AR ring to cross. I can't think of a single currently described weave that uses paired parallel.

Parallel Side Note: Parallel 5 is a 5 adjacent layer version of parallel. While still considered "parallel" it does result in different "weaves" from "standard" parallel (which could be designated as Parallel 3, but since parallel needs at least 3 layers of adjacent grain, putting 3 in the name would be redundant.) One example of parallel 5 can be found in the weave Assyrian.

Spiral Note: You may have noticed that there is no mirror version of spiral in the render above. It is my current belief that a continuous, paired grain mirror spiral cannot be made as part of a 3/4 chain or tube chain.

Tube Chain​

Tubes are the final chain form that can be made with the faceted modification. Their starting point is 2 cross grain chains (4 grains total) connected edge to edge. Most 4 grain tubes can also be broken up into two paired grains.

Tube chains can also be faceted further, usually with the addition of even numbers of grains. For example, here we have Half Persian 3 in 1, Full Persian 6 in 1, & Hilt. FP 6-1 and Hilt, in CCT, are considered Faceted Modifications of Half Persian 3 in 1. What some might find interesting is that the additional cross grain chains may change a weave form from having mirror pairs to having layered pairs (e.g. Full Persian 6 in 1 is mirror pairs while Hilt is layered pairs.)

Transformations - Making The Grains​

Grain transformations can be most easily defined as replacing one grain in a weave with another. Now that you've seen the different grains, it's time to show you how they're made and how simple it is to transform them into other grains.

Example Notes:

• The following examples are all cross grain chains.
• Cells will be connected using inversion locks.
• All examples are built to the right.
• Parallel grain will be shown last due to using a different cell structure from the other grains.
• In the following examples, the grains will be designated as a "Spinal" grain (stainless rings) and an "Inversion" grain (blue rings) for the purpose of differentiation.
  • The spinal grain (in these examples) will always be a lean grain (i.e. stainless rings are always positioned over the previous stainless ring).
  • The inversion grain will be used to show the transformation in step 4 (except for parallel which changes at step 3).

Lean Grain​

1. Start (as always) with a Root cell.
   
2. Invert the blue ring 180 degrees.
   
3. Connect an additional root cell to the inverted blue ring of the previous cell above the stainless ring.
   
4. Invert the blue ring clockwise OR counterclockwise and lock it inside the stainless ring of the previous cell.
   
5. Repeat steps 3 & 4 using the same clockwise OR counterclockwise inversion locks for the blue rings.
   

Congratulations, you just made:

Step Grain​

1. Start (as always) with a Root cell.
   
2. Invert the blue ring 180 degrees.
   
3. Connect an additional root cell to the inverted blue ring of the previous cell above the stainless ring.
   
4. Invert the blue ring clockwise OR counterclockwise and lock it inside the stainless ring of the previous cell.
   
5. Repeat step 3.
   
6. Invert the new blue ring in the opposite direction you used for the previous blue ring and lock inside the stainless ring of the previous cell.
   
7. Repeat steps 5 & 6.
   

Congratulations, you just made:

Twist Grain​

1. Start (as always) with a Root cell.
   
2. Invert the blue ring 180 degrees.
   
3. Connect an additional root cell to the inverted blue ring of the previous cell above the stainless ring.
   
4. Invert the blue ring clockwise OR counterclockwise and lock it inside the stainless AND blue rings of the previous cell.
   
5. Repeat step 3.
   
6. Invert the new blue ring in the opposite direction you used for the previous blue ring and lock inside the stainless AND the blue rings of the previous cell.
   
7. Repeat steps 5 & 6.
   

Congratulations, you just made:

Spiral Grain​

1. Start (as always) with a Root cell.
   
2. Invert the blue ring 180 degrees.
   
3. Connect an additional root cell to the inverted blue ring of the previous cell above the stainless ring.
   
4. Invert the blue ring clockwise OR counterclockwise and lock it inside the stainless AND blue rings of the previous cell.
   
5. Repeat steps 3 & 4 using the same clockwise OR counterclockwise inversion locks for the blue rings.
   

Congratulations, you just made:

Parallel Grain​

1. Start (as always) with a Root cell.
   
2. Invert the blue ring 180 degrees.
   
3. Connect a 1-2 cell to the inverted blue ring of the previous cell above the stainless ring.
   
4. Invert each blue cell opposing directions and lock in the stainless ring of the previous cell.
   
5. Connect an additional root cell to the inverted blue rings of the previous cell above the stainless ring.
   
6. Invert the blue ring (doesn't matter which direction) and lock it in the stainless ring of the previous cell, between the previous pair of blue rings.
   Please Note: This is NOT the "easiest" way to "physically" obtain the required result. It is however how it is explained in the interest of consistency. Based on CCT it is also what is happening regardless of how it is accomplished.
   
7. Repeat steps 3 - 6.
   

Congratulations, you just made:

Conclusion​

The preceding information should be enough to give you a solid foundation regarding grains and grain transformations. As I've stated in previous articles, I'm not a textbook/technical writer and CCT is constantly evolving. What this means is that information/definitions in this article (and the previous one) are tentative. Changes may be made in the case of new discoveries, changes in understanding, and/or better definitions. In such cases, the new information will be posted in the associated discussion thread, as well as updated in the article. There is still more to come, including more "in depth" articles about some of the concepts presented.

As always, if you have any questions or constructive criticism regarding CCT please feel free to let me know in the discussion thread for this article.

Appendix - Odds & Ends​

Alligator Back​

I cannot stress this enough, any two crossed grains will always form a cross grain chain when looked at on their own. The confusion this causes in the describing of weaves is the reason that one of the foundations of CCT is that rings cannot belong to more than one cell.

Take for example, the weave Alligator Back (AKA Euro-Persian Hybrid).

I've most commonly seen it referred to as European 4 in 1 with Half Persian 3 in 1 on the sides. While both are present, if we disassemble it, only one or the other can be present at a time. Lets take it apart, shall we?

• If I take away European 4 in 1, I'm left with 2 lean grains.
  
• If I take away both Half Persian 3 in 1 chains, I'm left with a single lean grain.
  
• If I take away a single Half Persian 3 in 1 chain, I'm left with a Half Persian 3 in 1 chain with a lean grain expansion, OR a 2 in 1 chain with a lean grain edge.
  
• if I take away a Half Persian 3 in 1 chain and a lean grain edge, I'm left with a 2 in 1 chain.
  

I guess this was my long winded way of showing that Alligator Back is more appropriately described as a band of European 4 in 1 with 3 in 1 Lean edging OR Mirrored Half Persian 3 in 1 chains with a 4 in 1 Lean spine.

Side Note: It also shows how Alligator Back is an edged progression of Iguana Back (which would be a band of European 4 in 1 with 2 in 1 Lean edging OR Mirrored 2 in 1 - Persian form chains with a 4 in 1 Lean spine.)

Grizzly​

Grizzly is a term that you may have seen before, mostly in reference to certain persian chains. In CCT, it is considered a sub-type of a grain transformation. Grizzly "weaves", in general, have had one grain manipulated into an unnatural position. Grizzly cross grain chains, without stabilization (or a very large AR) revert back to the natural form. Here we have Half Persian 3 in 1 in, one of, its "natural" forms (on top) and in it's "grizzly" form (on the bottom.)

Grizzly forms are differentiated from their "standard" forms by having the flared ends of all lean grains facing the same direction.

Transformation Examples in the Wild​

You can probably find lots of them out there, but here's one "series" and links to a couple of articles with quite a few more

• Lean -
  

  Band  Iguana Back

  • chainmaillers.com
  • Feb 12, 2023
  • Category: I
• Step -
  

  Band  Mystique

  • chainmaillers.com
  • Jan 8, 2023
  • Category: M
• Twist -
  

  Band  Vipera Berus 4 in 1

  • chainmaillers.com
  • Sep 26, 2020
  • Category: V

Additional Cellular Chainmaille Theory Articles​

• Introduction to the Basics: Creating a Chain
• Beyond The Basics
• Dilation Transformations