Introduction to the Basics: Creating a Chain

[chainmaillers.com]

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Introduction to the Basics: Creating a Chain - Introduction to the basic concepts of CCT through the creation of simple chains

Introduction​

Cellular Chainmaille Theory (CCT) is what I call the system that I use to structurally study weaves. While CCT started out as observations made while creating renders for the Maillepedia, it's evolved into much more than that (at least IMO). Certain elements and concepts have repeatedly made themselves apparent and changed the way that I look at weaves and how I define certain terms. Sections may have additional notes where CCT differs from, what I...

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[Karpeth]

Great writeup!

This is the best theory article on the basis of chainmaille I’ve seen. I have no criticism of the theory, except for the view of non-sharedness, but we’ve had that talk so many times.

The naming is a step - I have a hard time accepting some of your naming (mostly inverted), but I can not offer anything better.

Would you be open to me writing a counter-argument article (when you dive into cells)?

 

[chainmaillers.com]

Great writeup!

This is the best theory article on the basis of chainmaille I’ve seen. I have no criticism of the theory, except for the view of non-sharedness, but we’ve had that talk so many times.

The naming is a step - I have a hard time accepting some of your naming (mostly inverted), but I can not offer anything better.

Would you be open to me writing a counter-argument article (when you dive into cells)?

Thank you for the kind words, I have been working on it for a few years now

I hope that once it's all spelled out as a whole you'll see the method to my madness This article is really just showing the most basic of the "basics", but they can all be applied in more advanced ways. Much of the hold up in publishing about CCT is deciding what information goes together. The next article will cover other slightly more advanced applications of the basics (in a minimal manner) as well as other concepts that weren't necessary for making chains. Once the basics are done I hope to start posting articles that go further in depth on some of the topics.

I think it's more the combination of naming and concrete definitions of those terms and how they are applied. Hopefully you will come to accept it.

While you can certainly write a counter-argument article, it might be easier if you just post any questions or counters in the discussion thread for the original article (to keep everything grouped together) whenever it's written.

 

[Karpeth]

I am hoping to gather the strength to do a writeup on why the postulation ”Rings are NOT shared between cells” is wrong.

I’d furthermore like to see the ”root cell” theorisation being more fleshed out - currently, I have not seen the ”worth” of the view.

 

[Karpeth]

Not-share works for 4:4, cubes and chains - but not 6:3 imho. Had written something in an edit, but clicked cancel by mistake and it’s 2am, so I’ll see if I can write it tomorrow.

 

[moaatt]

This looks really good, however I have a few questions after reading it a few times:

1. Are units make of individual combinations of root cells? If so does that mean that all units in CCT have an even number of rings?
2. Are rotations of units along axes permitted under CCT? If not how do you account for weaves like Byzantine Square?

 

[chainmaillers.com]

This looks really good, however I have a few questions after reading it a few times:

Thanks for the compliment and being interested enough to ask questions.

1. Are units make of individual combinations of root cells? If so does that mean that all units in CCT have an even number of rings?

You're skipping ahead as I haven't covered units yet However, to answer your first part of your question, yes & no and as to the second part, to be honest, I haven't really counted. Offhand, I would have to say no, they will not always have an even number of rings.

To give you a teaser on units, there are currently 3 types of units recognized in CCT (and possibly a 4th, but haven't had time to do the research.

1. Ouroborus - when a chains end connects to the beginning. a seamless chain is essentially a really big unit.
2. Radial - when at least 3 isolated individual cells, weave cells, segments, and/or chains all radiate from a central ring.
3. Hybrid - when a seamless chain is connected to a central ring.

You're the second person to ask me something that really makes me wish I had more units posted in the Maillepedia (and the first to make me realize that I'm going to have to revamp many of the ones that I have based on the new system).

An example of an Ouroborus unit - Celtic Circle 3
An example of a Radial Unit - Inverted Aura Unit
An example of a Hybrid unit - Not Tao 3

2. Are rotations of units along axes permitted under CCT? If not how do you account for weaves like Byzantine Square?

Based upon the types of units that CCT recognizes, would you like to rephrase the question?

The way I explain Byzantine Square is another part of CCT that I haven't covered yet, "Expansions", which CCT considers a type of "Modification" (to be coveredl). As Byzantine Square is a sheet "Weave Form" (to be covered) the byzantine "Weave Cell" (to be covered) must also be modified to be able to be translated along two axis. This is done by adding a "Segment" (to be covered) of Byzantine to a weave cell of Byzantine (which can also be considered a terminated Byzantine chain (of fairly short length). Byzantine Square is essentially Japanese 4 in 1.

Side Note: There is a lot of overlap when it comes to weave cells, segments and units.

As I need to wake up in 4 hours I hope that answers your current questions. Please ask if you have anything else you would like clarified.

 

[moaatt]

Thank you very much for the detailed response, I can see that you have put a lot of thought into CCT and I find it extremely interesting. I do have some follow up thoughts/questions.

You're skipping ahead as I haven't covered units yet However, to answer your first part of your question, yes & no and as to the second part, to be honest, I haven't really counted. Offhand, I would have to say no, they will not always have an even number of rings.

To give you a teaser on units, there are currently 3 types of units recognized in CCT (and possibly a 4th, but haven't had time to do the research.

1. Ouroborus - when a chains end connects to the beginning. a seamless chain is essentially a really big unit.
2. Radial - when at least 3 isolated individual cells, weave cells, segments, and/or chains all radiate from a central ring.
3. Hybrid - when a seamless chain is connected to a central ring.

You're the second person to ask me something that really makes me wish I had more units posted in the Maillepedia (and the first to make me realize that I'm going to have to revamp many of the ones that I have based on the new system).

1. If units are not made of just combinations of root cells then it would make sense that it is possible for there to be units with non-even ring counts.
2. When do you plan on discussing the definition of a cell, I didn't see a definition in your original post though they were mentioned and I ended up making the assumption that a cell is a unit.

Based upon the types of units that CCT recognizes, would you like to rephrase the question?

The way I explain Byzantine Square is another part of CCT that I haven't covered yet, "Expansions", which CCT considers a type of "Modification" (to be coveredl). As Byzantine Square is a sheet "Weave Form" (to be covered) the byzantine "Weave Cell" (to be covered) must also be modified to be able to be translated along two axis. This is done by adding a "Segment" (to be covered) of Byzantine to a weave cell of Byzantine (which can also be considered a terminated Byzantine chain (of fairly short length). Byzantine Square is essentially Japanese 4 in 1.

Regarding this I think we may be using different definitions of "Translation". I am approaching this with the Euclidean geometry definition of translation (moving every point of a figure, shape or space by the same distance in a given direction). With this definition of a translation you would not be able to have units at right angles without rotations. Could you please clarify how you define a translation?

 

[chainmaillers.com]

1. If units are not made of just combinations of root cells then it would make sense that it is possible for there to be units with non-even ring counts.

The ouroborus unit example, Celtic Circle 3, is 21 rings.

2. When do you plan on discussing the definition of a cell, I didn't see a definition in your original post though they were mentioned and I ended up making the assumption that a cell is a unit.

It's not a far stretch to make that assumption since what each is has never really been defined. Many words are currently used interchangeably. Mind you, the definitions that I give are my definitions. For many the definitions may be different, or used for another term completely. The whole point of creating these articles is to show what is meant by these words and terms when used in CCT. I can't guarantee that anyone else will use it, although I hope they will. The only thing I can guarantee is that when I post I will be using these definitions.

At its most basic, the definition of a cell is "a grouping of connected rings used as a single element". While root cells are simply, and always will be, 2 connected rings, there are more advanced configurations that I plan to go over in the next article. As I define a unit, many of them can be used as weave cells. Weave cells are more of a type of cell that can be defined as a grouping of root cells that can be translated to create a weave form. As there are multiple weaves and multiple weave forms, each weave can have multiple weave cells associated with it.

I am approaching this with the Euclidean geometry definition of translation (moving every point of a figure, shape or space by the same distance in a given direction). With this definition of a translation you would not be able to have units at right angles without rotations.

There you go skipping ahead again That is, what I consider, an advanced application of CCT (that may be discussed "officially" way down the line). It's almost all rotations in some way In non advanced applications, for an expansion, the weave cell may need to be modified. This is the simplest example

At the top we have 1-1 chain (2 in 1 chain) where the weave cell is a root cell. if you translate the chain perpendicular to the axis of extension (an "Expansion") (the Y axis instead of the X axis), there is no connection between the chains.

At the bottom we have a modified 1-1 chain where the weave cell is a modified root cell. When that is expanded, we eventually get Japanese 4 in 1

And yes, you can say that the modified ring is a 90 degree rotation of ring 2 of the root cell around an axis central to ring 1 The modified root cell, by itself, can also be manipulated to be a "terminated root cell", a "radial 2 unit" or a "segment of 2 in 1 chain" (remember what I was saying about overlap )

 

[moaatt]

It's not a far stretch to make that assumption since what each is has never really been defined. Many words are currently used interchangeably. Mind you, the definitions that I give are my definitions. For many the definitions may be different, or used for another term completely. The whole point of creating these articles is to show what is meant by these words and terms when used in CCT. I can't guarantee that anyone else will use it, although I hope they will. The only thing I can guarantee is that when I post I will be using these definitions.

Ok, I can see where the outside term unit could bring some variance as it is not defined under CCT(in any published article). However, I think the layout of the information could be improved by defining some of the terms defined earlier or not referencing terms before they are defined.

At its most basic, the definition of a cell is "a grouping of connected rings used as a single element". While root cells are simply, and always will be, 2 connected rings, there are more advanced configurations that I plan to go over in the next article. As I define a unit, many of them can be used as weave cells. Weave cells are more of a type of cell that can be defined as a grouping of root cells that can be translated to create a weave form. As there are multiple weaves and multiple weave forms, each weave can have multiple weave cells associated with it.

This is interestesting I look forward to reading the next article(s) and seeing how it all comes together.

There you go skipping ahead again That is, what I consider, an advanced application of CCT (that may be discussed "officially" way down the line). It's almost all rotations in some way In non advanced applications, for an expansion, the weave cell may need to be modified. This is the simplest example

At the top we have 1-1 chain (2 in 1 chain) where the weave cell is a root cell. if you translate the chain perpendicular to the axis of extension (an "Expansion") (the Y axis instead of the X axis), there is no connection between the chains.

At the bottom we have a modified 1-1 chain where the weave cell is a modified root cell. When that is expanded, we eventually get Japanese 4 in 1

And yes, you can say that the modified ring is a 90 degree rotation of ring 2 of the root cell around an axis central to ring 1 The modified root cell, by itself, can also be manipulated to be a "terminated root cell", a "radial 2 unit" or a "segment of 2 in 1 chain" (remember what I was saying about overlap )

Ok, thank you for the clarification, I think part of the confusion is that I forgot about the discussion of rotation in Invererted root cells for a bit.