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The Tessellation Theory of the Voodoo Weaves
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The Tessellation Theory of the Voodoo Weaves
Article © MAIL User: Drax
Tessellation Theory of the Voodoo Weaves
It's time to take another look at how tessellation theory sits at the core of yet another set of weaves: the Voodoo weaves. If you haven't already, take a look at my article on how the Japanese weaves directly draw from tessellations: The Tessellation Theory of Japanese Weaves.
To define the term again, a tessellation usually refers to a type of mosaic. Most often, though not always, these mosaics derive from the symmetric arrangement of regular shapes (triangles, squares, hexagons, etc).
As mentioned in the article on Japanese weaves, Japanese 4 in 1 is patterned after a grid of squares (like graph paper). It turns out that Voodoo is basically Japanese 4-1. I'll explain in more detail how this works, and the rest should easily follow.
Imagine a patch of Japanese 4-1 (usually done with large main-rings and smaller linking-rings). Now swap sizes -- make the linkers large and make the 'main' rings small. Finally, interlock every linker ring in a moebius fashion where the 4 linkers come together. Voila -- you now have Voodoo, very different in appearance than Japanese 4-1, but a simple transformation.
It is this transformation that relates Voodoo weaves to tessellation theory. In this case, we can make our Voodoo-family weaves by putting a moebius center at every tessellation vertex. However, this time, there's a little trick thrown in to make things more complicated. In Voodoo-family weaves, a moebius center must have the opposite handedness of all of its connected neighbors.
As you may know, there are two ways to form moebius balls (much for the same reasons you can have two different directions for spirals, or two different directions for Half-Persian chains). For the purposes of this article, I'll be calling them CW (clockwise) and CCW (counter-clockwise) centers; look at a moebius center in Voodoo and determine what direction the rings spiral out of the middle, and that's what I'm calling it.
If you look at a patch of Voodoo, you will notice that all of the moebius centers alternate right- and left-handedness. To represent this in grid-form, it would look like the following:
where the red "X" represents CW centers and blue "O" represents CCW centers. In this picture, it's easier to see how they alternate -- that is, every center is surrounded (or connected to) a center of opposite handedness.
If you want to turn a tessellation pattern into a Voodoo-style weave, then you must be able to form this alternating pattern of moebius centers. If not, then the tessellation pattern will not work in Voodoo-style. For instance, Japanese 6 in 1, or the arrangement of triangles, cannot have a Voodoo equivalent.
In fact, any tesselation with small triangles will not work, nor any other pattern with odd-numbered polygons (pentagons, heptagons, etc). You cannot alternate two items around an odd-numbered figure and create a continuous loop -- there will always be an area where you have two of the same symbols in a row (shown by the purple X above), and that won't mesh with Voodoo's need for alternating centers. There are not a lot of tessellation patterns with odd-numbered polygons, except for triangles -- and there's lots with triangles. So unfortunately there's a lot of tessellation patterns that won't work with Voodoo (at least you can still use them in Japanese weaves!). Also, you won't be able to create a Voodoo buckeyball (soccerball) because that design incorporates pentagons (rats!).
Let's see some more examples to hammer this idea home.
Voodoo Hexagonal derives from a grid of hexagons. Its Japanese equivalent is Japanese 3 in 1.
I "created" a new weave using this technique. The pattern derives from the classic pattern of octagons and squares (the Japanese equivalent is listed as sakredchao's Japanese 3 in 1 Octagon / Square Tessellation). It kinda looks like tiny square-units of Voodoo hung at the corners, alternating orientation. It also squishes into a form that looks like basic Voodoo, but with some rings missing. I've called it Voodoo Net.
Finally, I could resist "creating" one more and so here's my final example:
It derives from the Hizashi2 weave that I mention in my other articles on tessellation theory. I never made the Japanese version of this weave in actual rings, so I thought I'd give it a go in Voodoo-style. As you can see, this pattern does have "triangles", but the triangles have 6 moebius centers along their perimeter, thus making them viable for Voodoo-weaving.
The extension of Voodoo-style weaving into tessellations doesn't open up as many possibilities as compared to Japanese-style weaving (due to the restriction of even-numbered polygons), but I found the basis intriguing enough to write up the information. Of course, all of this information will work with the Hoodoo style as well (since Hoodoo is Voodoo without the little connector rings). Maybe somebody will find the information useful and be able to make something new and wonderful from it. Thanks for reading!
It's time to take another look at how tessellation theory sits at the core of yet another set of weaves: the Voodoo weaves. If you haven't already, take a look at my article on how the Japanese weaves directly draw from tessellations: The Tessellation Theory of Japanese Weaves.
To define the term again, a tessellation usually refers to a type of mosaic. Most often, though not always, these mosaics derive from the symmetric arrangement of regular shapes (triangles, squares, hexagons, etc).
As mentioned in the article on Japanese weaves, Japanese 4 in 1 is patterned after a grid of squares (like graph paper). It turns out that Voodoo is basically Japanese 4-1. I'll explain in more detail how this works, and the rest should easily follow.
Imagine a patch of Japanese 4-1 (usually done with large main-rings and smaller linking-rings). Now swap sizes -- make the linkers large and make the 'main' rings small. Finally, interlock every linker ring in a moebius fashion where the 4 linkers come together. Voila -- you now have Voodoo, very different in appearance than Japanese 4-1, but a simple transformation.
It is this transformation that relates Voodoo weaves to tessellation theory. In this case, we can make our Voodoo-family weaves by putting a moebius center at every tessellation vertex. However, this time, there's a little trick thrown in to make things more complicated. In Voodoo-family weaves, a moebius center must have the opposite handedness of all of its connected neighbors.
As you may know, there are two ways to form moebius balls (much for the same reasons you can have two different directions for spirals, or two different directions for Half-Persian chains). For the purposes of this article, I'll be calling them CW (clockwise) and CCW (counter-clockwise) centers; look at a moebius center in Voodoo and determine what direction the rings spiral out of the middle, and that's what I'm calling it.
If you look at a patch of Voodoo, you will notice that all of the moebius centers alternate right- and left-handedness. To represent this in grid-form, it would look like the following:
where the red "X" represents CW centers and blue "O" represents CCW centers. In this picture, it's easier to see how they alternate -- that is, every center is surrounded (or connected to) a center of opposite handedness.
If you want to turn a tessellation pattern into a Voodoo-style weave, then you must be able to form this alternating pattern of moebius centers. If not, then the tessellation pattern will not work in Voodoo-style. For instance, Japanese 6 in 1, or the arrangement of triangles, cannot have a Voodoo equivalent.
In fact, any tesselation with small triangles will not work, nor any other pattern with odd-numbered polygons (pentagons, heptagons, etc). You cannot alternate two items around an odd-numbered figure and create a continuous loop -- there will always be an area where you have two of the same symbols in a row (shown by the purple X above), and that won't mesh with Voodoo's need for alternating centers. There are not a lot of tessellation patterns with odd-numbered polygons, except for triangles -- and there's lots with triangles. So unfortunately there's a lot of tessellation patterns that won't work with Voodoo (at least you can still use them in Japanese weaves!). Also, you won't be able to create a Voodoo buckeyball (soccerball) because that design incorporates pentagons (rats!).
Let's see some more examples to hammer this idea home.
Voodoo Hexagonal derives from a grid of hexagons. Its Japanese equivalent is Japanese 3 in 1.
I "created" a new weave using this technique. The pattern derives from the classic pattern of octagons and squares (the Japanese equivalent is listed as sakredchao's Japanese 3 in 1 Octagon / Square Tessellation). It kinda looks like tiny square-units of Voodoo hung at the corners, alternating orientation. It also squishes into a form that looks like basic Voodoo, but with some rings missing. I've called it Voodoo Net.
Finally, I could resist "creating" one more and so here's my final example:
It derives from the Hizashi2 weave that I mention in my other articles on tessellation theory. I never made the Japanese version of this weave in actual rings, so I thought I'd give it a go in Voodoo-style. As you can see, this pattern does have "triangles", but the triangles have 6 moebius centers along their perimeter, thus making them viable for Voodoo-weaving.
The extension of Voodoo-style weaving into tessellations doesn't open up as many possibilities as compared to Japanese-style weaving (due to the restriction of even-numbered polygons), but I found the basis intriguing enough to write up the information. Of course, all of this information will work with the Hoodoo style as well (since Hoodoo is Voodoo without the little connector rings). Maybe somebody will find the information useful and be able to make something new and wonderful from it. Thanks for reading!
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