Ring Interaction Model (R.I.M) (long article)
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Ring Interaction Model (R.I.M) (long article)
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Posted on Thu Nov 15, 2012 5:20 pm
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Imagine - every time you start a chainmaille project, you start with one ring. This one ring is the corner stone of all chainmaille weaves. Then, you connect another ring to that first ring. These two rings have to connect to each other, there are no other combinations of connections. Then you add a third ring. Now there are more possibilities for interactions. You can make Straight 2 in 1, you can make a Mobius Knot, or you can make an Orbital interaction. Depending on the aspect ratios of the rings, you can make an infinite number of outcomes, but they will always be a version of Straight 2 in 1, Mobius, or Orbital. There are no other mathematical combinations for 3 rings. Then you add a fourth ring variable. Now there are many more combination possibilities. The table I created, called the "Ring Interaction Model (R.I.M)" shows all of the connection possibilities at levels 1-4 (level = # of rings in the interaction). The R.I.M shows levels 1-4, but will hopefully someday include level 5 as well. The mathematical possibilities for ring interactions seems to grow exponentially as the level increases. So, level 5 will likely include 100-500 possible combinations and the table that includes all of these would be huge. On my website, you can download a free pdf of the R.I.M here to look at as you read this article:

http://www.joshuadiliberto.com/WEAVEINFORMATION.html

The R.I.M. was inspired by the periodic table of elements. Think of each interaction as an element. It is meant to be a guide to the building blocks of all ring interactions where the resulting interactions are stable - in that no ring can fall off.  As chainmaillers, we know that a weave is a repeating pattern of possible connections as we add rings or levels. At what point we choose to start repeating, with what connection, and with what size ring, is what makes weaves different from others. The R.I.M takes into account every possible connection (whether repeating or not) with every possible aspect ratio. In other words, every weave must start with a connection listed in the R.I.M. No weave falls outside the R.I.M. Interactions that are not possible are not listed in the R.I.M.

It is debatable whether Orbital is a “connection” since the orbiting ring is not connected to any ring.  This is why the table in called "Ring Interaction Model" and not "Ring Connection Model."  The model simply shows and labels all interactions that are mathematically possible/stable and lets the user decide for themselves how they want to interpret it for their own weave theory.  For example: someone could hold the belief that a right handed Mobius and a left handed Mobius are different interactions. The R.I.M. doesn't say whether they are or not, it just shows a picture of a 3 and 4 ring Mobius Knots and labels them with an (h) that indicates that it has right and left handed versions.

The R.I.M. doesn't name weaves. Weaves are called by many different names. The R.I.M. strictly adheres to mathematical possibilities of connections. Example: you can see Half Persian 3 in 1 start to form in “4-4” of the R.I.M., but there is no name listed in the picture. The naming of Half Persian 3 in 1 is up to the user.

The R.I.M. is intended for use by the international chainmaille community. Instead of naming a weave, it lists a combination possibility in a table that every can use and agree on. The R.I.M. is not intended to replace weave naming or current categorization attempts. In my opinion, it does have potential for weave categorization, but current methods that have stood the test of time should be honored. I don't think anyone would like to see European 4 in 1 renamed as something like “5-1.” I think the R.I.M. can best be used as a tool for creating new weaves. As the user attempts ring combinations, he/she will start to see new and interesting ways to connect rings in repeating patterns. The R.I.M. can also be a tool for understanding ring connections: through eye (te), around eye (ae), no eye (ne), and orbital (o). There are other ring connections that do not yet present themselves in levels 1-4, so are not listed in the R.I.M. This is another reason why completing level 5 in the R.I.M. would be valuable.

Explaining level 4: The interactions in level 4 are all the mathematical combinations of 4 rings.  The columns are lined up in a way that shows how they can be built from the interactions above them in level 3.  If the column is situated between two interactions in level 3, then those interactions can be built from either interaction in level 3.  The columns are also organized by "h" handed and "s" symmetrical.  If an interaction is handed, then it has no symmetry and the ring orientations have a structure of left or right handed.  Example: left and right handed Half Persian 3 in 1 or right and left handed Mobius Knots.  If an interaction is symmetrical, then it has at least 1 plane symmetry – the image in size and arangement of rings is the same on either side of the plane that splits the interaction in a given direction in 3 dimensions.

The model shows the interactions where all rings have the same aspect ratio.  It lists the mathematical minimum for the ring interaction when all rings in the connection have the same aspect ratio (example: >2).  I am still working out the mathematical accuracy of these figures. Currently, the values are rounded to the nearest whole number. The R.I.M. lists the Orbital connection as needing rings that are >5, but in actuality the more accurate value is >5.4. The model is not limited by - all the rings being the same size though.  Yes, the minimum aspect ratio value is no longer valid when the rings' aspect ratios change, but the number of possible interactions remains valid.  There are 2 exemptions to this that I have found in the model. They are in level 4 and indicated with a (*) and a (**).  The first (*) exception is if you have 3 rings in a row with “ne” connections and 1 ring orbiting between one of the connections (as in “4-15” and “4-19” of the R.I.M.).  If the middle ring shrinks and goes down in aspect ratio, eventually the orbiting ring will be able to slip over it and be able to move to the other side (as in “4-19”), yet is still bound in the overall interaction of rings.  This exception is visible in Orbit, Dragon Tail, and Shenanigans.  The other (**) exception is in the bottom right corner “4-18”.  It shows 2 rings with (ne) connections, 1 orbiting between them, and one ring with a (ne) connection to the orbiting ring.  If the interaction has all rings that are between aspect ratio 5 and 7, the ring that connects to the orbiting ring is locked into a quadrant and the connection becomes (h) handed.  If the ar of the interaction is above 7, then the ring that connects to the orbiting ring can move freely in all 4 quadrants and is then classified as (s) symmetrical. That is why the symmetrical/handed box contains (**) - it is conditional. As far as i can tell, these are the only exceptions in level 4. I would like to get feedback from the community as to whether these are the only exceptions in level 4. Level 5 would have many more exeptions. This posses a problem for completing an accurate table. A few exeptions are acceptable and even interesting, but 20 exceptions would be rediculous and make the R.I.M cumbersome to interpret. By completing level 5, I may find that there is a new and better way of categorizing exceptions, but there is no way to know until it is tried.

My predictions: level 5 would be a huge undertaking and could possibly account for 90% -100% of all interactions and weaves in the database of M.A.I.L.  I'm guessing that the number of interactions in level 5 would be in the hundreds - somewhere between 100 and 500.  I've tried to figure, mathematically, how many interaction possibilities would be in level 5 and I can't seem to get an accurate answer.  There are just too many variables. This is largely due to an effect that presents itself in level 4 of the model.  As the ring number/level rises, the possible number of multiple ring interactions with infinite aspect ratios exponentially grows.  Since there are an infinite number of aspect ratio combinations in an interaction, it is difficult or impossible to know what interactions and exceptions it will yield without actually trying them.  It is much easier to figure the possibilities if all the rings have the same aspect ratio and then jump into the exceptions of different aspect ratios within an interaction later.  

What could this model do for weave cataloging and organizing?  If you look at this model purely as an interaction model, then the answer is "nothing."  If you look at this model as a guide for how all weaves begin, then it can do a lot.  For example, if you look at each level individually, you can say "all weaves come from these interactions."  Level three is the first split where the interaction options are more than 1.  So, you could categorize all weaves from the 3 interactions on level 3 and call them “3 families.”  Then, you could say that the options in level 4 are "sub-families" of level 3.  All exceptions would be accounted for, no weave would or could fall outside of the R.I.M. Since there is no naming of weaves in the R.I.M., it wouldn't matter when stable European 4 in 1 presented itself because it would be present in many different interactions. Example: you can see European 4 in 1 start to form in “4-3,” but only because of the way the rings are layed out in the picture. In actuality, “4-3” is just two rings connected to 2 rings with (ne) connections. Whether or not European 4 in 1 is represented in the R.I.M. is irrelevant. It only shows every mathematical combination of rings. Seeming complications like - weaves that display multiple interactions - are easily explained as having multiple origins that are clearly displayed in the R.I.M.  I don't think many people would be excited by this though. Weaves would no longer have names, instead they would have number signatures in multiple interactions within the R.I.M.  Since the model is purely mathematical, it shows no preferential treatment to historical or cultural weaves. I happen to think history and culture are very important, and I think others do as well.

Please let me know your thoughts about the R.I.M. and any constructive criticism on table organization would be great.  Thanks so much for listening and for your feedback.

-The Mithril Weaver
-Josh 



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Re: Ring Interaction Model (R.I.M) (long article)
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Posted on Fri Nov 16, 2012 12:00 am
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mithrilweaver wrote:
Then, you connect another ring to that first ring. These two rings have to connect to each other, there are no other combinations of connections.

I know I'm quibbling... but this is not true. I would consider wording this another way. It is quite possible to make a weave starting with two rings that are not connected. It isn't until the third ring that a connection is usually required, although it's even possible for a weave to start with more than three unconnected rings.


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Posted on Fri Nov 16, 2012 12:04 am
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I think you might be over exaggerating level 5, I've done this once before and changing the AR doesn't offer many more possibilities, changing the shape and size of the ring would offer infinite possibility.

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Posted on Fri Nov 16, 2012 12:55 am
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My comment doesn't really have to do with the theory - as I've said many time that most of weave theory goes WAY over my head - but rather, I have a problem with the font you've chosen. Even zoomed in, I can mostly read the things in the cells but the notes you have at the bottom are pretty near intelligible to me because of the way the letters run together.

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Re: Ring Interaction Model (R.I.M) (long article)
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Posted on Fri Nov 16, 2012 1:15 pm
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lorraine wrote:
mithrilweaver wrote:
Then, you connect another ring to that first ring. These two rings have to connect to each other, there are no other combinations of connections.

I know I'm quibbling... but this is not true. I would consider wording this another way. It is quite possible to make a weave starting with two rings that are not connected. It isn't until the third ring that a connection is usually required, although it's even possible for a weave to start with more than three unconnected rings.


so, you're saying it is possible to make a weave starting with two rings that are not connected? regardless of whether or not the individual starts with more than one ring not directly connected, eventually they are connected. every weave can be torn down to 4, 3, 2, and 1 ring. just like it can be built up from the same. yes, it's not true that the individual has to start with two rings connected, but that's not the point of the theory. i'm looking at conceptual ring theory here, not individual's preference for connecting rings. i thought this was pretty obvious, but maybe i should word that in the opening paragraph?



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Posted on Fri Nov 16, 2012 1:24 pm
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Jax25 wrote:
My comment doesn't really have to do with the theory - as I've said many time that most of weave theory goes WAY over my head - but rather, I have a problem with the font you've chosen. Even zoomed in, I can mostly read the things in the cells but the notes you have at the bottom are pretty near intelligible to me because of the way the letters run together.


yes, making the font more visible is something i would like to work on. thx.



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Posted on Fri Nov 16, 2012 1:31 pm
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djgm wrote:
I think you might be over exaggerating level 5, I've done this once before and changing the AR doesn't offer many more possibilities, changing the shape and size of the ring would offer infinite possibility.


do you have a estimate for how many combinations level 5 has? i started thinking that it would be about 50 or so, but then when i lookied at interaction "4-1" and started adding a 5th ring in different combinations, i came up with about 15 different combinations for just one interaction on level 4. so, when i extend that to all the other interactions, i get 15x19 = 285 combinations. this is just an estimate. how did you get your estimate?



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Posted on Fri Nov 16, 2012 3:11 pm
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by level 5 we are talking about 5 links right? so lets think about it,
one link=1 link
two links=1 connection
three links= 3 connections (chain, mobi, orbit)
four links= 15 connections (chain,chain with kinged end, rounded chain, mobi,three link mobi one kinged, three link mobi with a dangler, three link mobi with dangler connect to two links, three link mobi with dangler connected to one flipped link and one not fliped, three link mobi with dangler connected to two flipped links, spiral 4in1, persian, orbit with extra link on chain, orbit with extra link on orbit, kinged orbit) maybe more this game isnt fun.

then after that all kinds of wild possibilities open up like spiral 6in1 for example, but if I always have to go back and reference existing info to make my point I'm not bringing anything new to the table. the other thing is working with such small samples of connections does little to clarify the issue in the mind of a beginner fiddling floppy masses of links around.

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Posted on Fri Nov 16, 2012 4:01 pm
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djgm wrote:
by level 5 we are talking about 5 links right? so lets think about it,
one link=1 link
two links=1 connection
three links= 3 connections (chain, mobi, orbit)
four links= 15 connections (chain,chain with kinged end, rounded chain, mobi,three link mobi one kinged, three link mobi with a dangler, three link mobi with dangler connect to two links, three link mobi with dangler connected to one flipped link and one not fliped, three link mobi with dangler connected to two flipped links, spiral 4in1, persian, orbit with extra link on chain, orbit with extra link on orbit, kinged orbit) maybe more this game isnt fun.

then after that all kinds of wild possibilities open up like spiral 6in1 for example, but if I always have to go back and reference existing info to make my point I'm not bringing anything new to the table. the other thing is working with such small samples of connections does little to clarify the issue in the mind of a beginner fiddling floppy masses of links around.


yes, the sequence goes 1,1,3,19,? the hard part is - depending what theory you use, level 3 could have between 2 and 4 different combinations - straight 3, mobius left, mobius right, and orbital. level 4 can have about 30 different combinations depending on the theory used. in the r.i.m., i condensed the right and left versions and then labeled them (h) - bringing the number down to 19 combinations or 18 and 1 exception. listing every right and left handed version for level 5 would result in well over 200 combinations. i think i can bring it down to 100 - 150 by condensing. the interesting thing is, there have got to be some new weaves in level 5 that no one has documented. just by completing level 5, one could start designing lots of new weaves.



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Posted on Fri Nov 16, 2012 9:30 pm
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mithrilweaver wrote:
Jax25 wrote:
My comment doesn't really have to do with the theory - as I've said many time that most of weave theory goes WAY over my head - but rather, I have a problem with the font you've chosen. Even zoomed in, I can mostly read the things in the cells but the notes you have at the bottom are pretty near intelligible to me because of the way the letters run together.


yes, making the font more visible is something i would like to work on. thx.


Oh good! Smile And I noticed I typo'd a couple times in there. Of course I meant "near unintelligible"...but I figure you got that.

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Re: Ring Interaction Model (R.I.M) (long article)
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Posted on Sat Nov 17, 2012 12:31 am
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[quote:a1fc8742fc="mithrilweaver"][quote:a1fc8742fc="lorraine"][quote:a1fc8742fc="mithrilweaver"]Then, you connect another ring to that first ring. These two rings have to connect to each other, there are no other combinations of connections.

I know I'm quibbling... but this is not true. I would consider wording this another way. It is quite possible to make a weave starting with two rings that are not connected. It isn't until the third ring that a connection is usually required, although it's even possible for a weave to start with more than three unconnected rings.


so, you're saying it is possible to make a weave starting with two rings that are not connected? regardless of whether or not the individual starts with more than one ring not directly connected, eventually they are connected. every weave can be torn down to 4, 3, 2, and 1 ring. just like it can be built up from the same. yes, it's not true that the individual has to start with two rings connected, but that's not the point of the theory. i'm looking at conceptual ring theory here, not individual's preference for connecting rings. i thought this was pretty obvious, but maybe i should word that in the opening paragraph?
What I said was you should consider rewording that part because, while I understand what you are saying, others less familiar with weave theory may not. The idea is to communicate information in your article, is it not? I am simply pointing out that what you consider "obvious" may not be obvious to everyone else reading your article.

Arkham See the first two copper rings? They are never connected to each other. They are only connected to rings woven after them. This is an example of how your wording can be misunderstood.

There are people who do not understand the difference between weave theory and weaving instructions. I have found this to be true in other discussions here on MAIL and on other forums. Taking the chance of losing your reader's understanding of what your article is about in the first paragraph is not good, in my opinion. My suggestion was meant as constructive criticism to help make it better understood and had nothing to do with either conceptual ring theory or an individual's preference for connecting rings.


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Re: Ring Interaction Model (R.I.M) (long article)
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Posted on Sat Nov 17, 2012 3:00 pm
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[quote:1a5b4ae17a="lorraine"]There are people who do not understand the difference between weave theory and weaving instructions. I have found this to be true in other discussions here on MAIL and on other forums. Taking the chance of losing your reader's understanding of what your article is about in the first paragraph is not good, in my opinion. My suggestion was meant as constructive criticism to help make it better understood and had nothing to do with either conceptual ring theory or an individual's preference for connecting rings.


This article is conceptually advanced. Most newbies wouldn't get too far into it before realizing this and moving on to something else.

The first sentence begins with the word "imagine", which puts forth a hypothetical. It doesn't state that the second ring HAS to be added to the first in every possible instance, and I don't find it to read that way.

Is it that you think someone may start reading this article and perhaps stop because it's too much for them to handle (or even possibly read the whole thing), later deciding to try a weave tutorial, such as Arkham, which happens to have the first few rings not connect to each other, and then decide not do it because they think it's the wrong way to weave, just because they read the hypothetical statement laid out in the first sentence of this article?


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Posted on Sat Nov 17, 2012 6:34 pm
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the other thing is any pattern or connection style that emerges in level 4 has to be overlooked in level 5 in the hunt for this new weave.

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Re: Ring Interaction Model (R.I.M) (long article)
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Posted on Sat Nov 17, 2012 10:55 pm
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[quote:e307570a89="Chainmailbasket_com"][quote:e307570a89="lorraine"]There are people who do not understand the difference between weave theory and weaving instructions. I have found this to be true in other discussions here on MAIL and on other forums. Taking the chance of losing your reader's understanding of what your article is about in the first paragraph is not good, in my opinion. My suggestion was meant as constructive criticism to help make it better understood and had nothing to do with either conceptual ring theory or an individual's preference for connecting rings.


This article is conceptually advanced. Most newbies wouldn't get too far into it before realizing this and moving on to something else.

The first sentence begins with the word "imagine", which puts forth a hypothetical. It doesn't state that the second ring HAS to be added to the first in every possible instance, and I don't find it to read that way.

Is it that you think someone may start reading this article and perhaps stop because it's too much for them to handle (or even possibly read the whole thing), later deciding to try a weave tutorial, such as Arkham, which happens to have the first few rings not connect to each other, and then decide not do it because they think it's the wrong way to weave, just because they read the hypothetical statement laid out in the first sentence of this article?
I was reading the article from an editor's point of view. My suggestion wasn't really about weave theory or tutorials specifically. I referenced a tutorial because I was trying to explain what I was talking about (which I shouldn't have done because it only confused things). I was making a trivial editing comment. It was not meant to be taken as a seriously grievous error. I said I was "quibbling" in the first sentence of my post, and that's how it was meant. No other reasons apply.


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Posted on Sun Nov 18, 2012 7:10 pm
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Heck, I'm not a newbie and I stopped reading somewhere in the second paragraph and went to look at the table itself. Razz

Though I do have a severe case of AD-oooh, shiny!

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