Cellular Chainmaille Theory Beyond The Basics

Introduction​

Translations - Part II​

You didn't think extensions were the only type of translation that can be done, did you?.

Expansion​

Expansions are when you take an extension and translate on an axis that is perpendicular to the axis of extension. Expansions are used to make bands and sheets

Elevation​

Elevations are when you take an expansion and translate on an axis that is perpendicular to the axis of extension and the axis of expansion. Elevations are one way of making 3D Objects.

Translation Notes:​

• Expansions may require modification to the extension before being translated.
• Elevations may require modification to the expansion before being translated.
• Expansions and Elevations are considered Modifications

Cell & Segment​

Cell​

Base Cells​

Weave Cells​

Weave Cell Notes:​

• Other than in the case of spiraling weaves, weave cells are always translated without rotation.
• While many different weaves may use the same base cell(s), the cellular connections between the base cells will differ, resulting in different weave cells.
• Weaves may have more than one weave cell.

Segment​

An incomplete grouping of connected rings from multiple cells present in a weave. Segments can be taken from all weave forms.

Weave Forms​

Weave forms are the different ways that we, as chainmaillers, present weaves. Weave Cells may need to modified to allow for the translations necessary for the different weave forms. CCT recognizes four primary weave forms:

• Unit​

  Weave form where translations are done around a central origin ring(s) or point. Units start with 3 elements + the origin.

• Chain​

  Weave form where translations are done along a single axis and connected to the previous cell. (Extension)

• Sheet​

  Weave form where translations are done along two axis. (Extension & Expansion) The second translation is done along an axis perpendicular to the first and connected to the previous extension. Sheets are expanded chains.

• 3D Object​

  Weave form where translations are done along three axis. (Extension, Expansion, & Elevation) The third translation is done along an axis perpendicular to both the first and second and connected to the previous expansion OR where translations result in a sphere around a central point.

Weave Form Notes:​

• There are multiple weave sub forms including (these definitions may be refined and/or revised):
  • Radial Unit - When at least 3 isolated elements all radiate from a central ring(s).
    
    
  • Loop Unit - When a chains end connects to its' beginning. A loop unit requires at least 3 elements. Yes, a seamless chain is essentially a really big loop unit.
    
    
  • Hybrid Unit - When a loop unit is reinforced by a central ring(s). Can also be seen as a radial unit where the radial elements are not isolated from each other.
    
    
  • 3/4 chain - The mid point between a chain and a tube or a chain and a band.
    
    
  • Tube - At least two chains rotated around a central axis and connected to each other on their edges. Connection of the chains may be done with a modification.
    
    
  • Band - At least two chains connected on a single edge, or an expansion termination of a chain, In bands the extension is longer than the expansion.
    
    
  • Cross Band - At least two chains connected on a single edge. In cross bands the expansion is longer than the extension.
    
    • Band Notes
      • Bands (both types) that are not terminated can be further expanded into sheets.
  • Web Sheet - Still not really sure how to describe this, but don't want to hold up publishing the rest of the information. What are currently classified as "Web Sheets" can, for now, be found here.

Weave Classes​

Weave classes are the major categories that weaves belong to. Weaves can belong to multiple categories:

Progression​

Modifications​

• Expansion - An extension translated on an axis that is perpendicular to the axis of extension.
• Elevation - An expansion translated on an axis that is perpendicular to the axis of extension and the axis of expansion.
• Faceted - Addition of a grain(s) to an edge of a chain that is normally a layer or mirror of an existing grain.
  
  
• Reinforced - Addition of a ring(s), creating a new connection(s) to reinforce specific positioning of existing rings.
  
• Modification Notes:
  • Expansions and Elevations are considered modifications because they are adding new rings and connections on an edge where they were previously not present.

Transformations​

• Dilation - The use of two different ring sizes in root cells (this may not be the final definition), e.g. in CCT Dragon Tail is considered a dilation of Half Persian 3 in 1.
  
  
• Grain - Replacement of a grain with a different grain, changing the direction of a grain or an existing ring in a cell.
  
  
• Oblique - Making a connection between two rings, that did not previously exist, from a pair of rings that were not previously connected, e.g. in CCT Cross Eyed Persian is considered an oblique of Full Persian 6 in 1.
  

Variations​

• Captive - The addition of an element that is held in place by surrounding rings without connecting with them.
  
  
• Mobized - The replacement of a single ring with a 3 (or more) ring mobius, used as a single ring.
  
  
• Nested - The addition of a ring(s), on the same plane, inside or outside of a ring, used as a single ring. Commonly known as "Scaled".
  
  
• Orbital - The addition of a ring(s) around a ring, the internal connection of a cell, or a cellular connection between cells.
  
  
• Stacked - The addition of a ring(s), on the same plane, above or below and/or in front of or behind a ring, used as a single ring. Commonly known as "Kinged".
  

Odds & Ends​

Grains​

1. Adjacent
   
2. Lean
   
3. Step
   
4. Parallel
   
5. Twist
   
6. Spiral
   

Grain Note: All grains other than Twist and Spiral devolve into a pile of rings without an additional cross grain. Twist and Spiral devolve into 2 in 1 chain.

Additional Notes​

Base cells - the definition above will probably be updated at some point. I believe that it may currently be too inclusive. The following render shows other "base cells" based only upon the "stacking" variation, however that might be too restrictive.


Base weaves - Base weaves are definitely a weave class, but too many weaves would be included as "Base Weaves" based upon the current definition of base cells.

Segmented - Segmentation does occur, but it is still under investigation whether it should be considered a modification, transformation, or variation.

Units - You may have noticed that units have a requirement of 3 elements + origin. This is in the interest of clearing up some major overlap between units, cells and segments. When looked at individually (which is what CCT is all about) a radial unit with only the origin and 1 element (radial 1) could be a root or base cell and/or a segment, and a radial unit with only the origin and 2 elements (radial 2) could be a base cell, weave cell and/or a segment.

Conclusion​

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.