Ring Interaction Model (R.I.M) (long article)
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mithrilweaver

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Posted on Mon Nov 19, 2012 3:30 pm

 mithrilweaver wrote: it's really hard not to end a sentence with an acronym. my language skills are very poor.

An easy solution I see to this is to stop putting all the periods in the acronym. Call it the "RIM" instead of the "R.I.M."

Just a thought...
symmetry

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 Posted on Mon Dec 03, 2012 5:51 am Link to Post: Nifty! (Actually when I think about weave classification from time to time, and play, it's more in terms of incidence matrices. Entries 0, 1, or -1 to account for the two possible directions (counter-clockwise or clockwise) which one ring could intersect another, if they do intersect. Then there's the problem of what constitutes a valid/useful normal form, and what transformations are valid between two incidence matrices, that will get us to the normal form. There's also the fact that the number of possibilities can conceivably go up exponentially with the number of rings in a cluster (each pair may intersect clockwise, counterclockwise, or not at all, so possibly as many as 3^n possibilities... though some will be equivalent to each other). In other words, the table will likely get very large, very fast. So maybe good to classify the smaller clusters explicitly, more hardcore theory for the larger ones. And of course there's also the issue of how to deal with the way clusters (units related by translations along a chain or sheet or space) connect. One example would be the same cluster of 6 (2-2-2) rings that, depending on how units are connected, could turn into simple 4 in 2 chain, or Byzantine. Something simpler, like maybe a refined version of the table you offer, would possibly work better for most people here, though. Though I'm kinda hoping that at least one other person here has enough knowledge of linear algebra and group theory or graph theory to have some glimmering of what I'm getting at :) (hi again to those who remember me; vision problems took me away from chainmailling for a while)

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 Posted on Mon Dec 03, 2012 4:28 pm Link to Post: Most of what you said was gibberish to me (I never liked math, though I've been told repeatedly that I have an aptitude for it) but I just wanted to say, "Weclome back, symmetry!!" Glad to see you again.
symmetry

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 Posted on Mon Dec 03, 2012 7:06 pm Link to Post: Jax25: Aw, thanks :) Mostly I was talking about a way in which one could represent various clusters of rings in terms of the ways in which pairs of rings intersect, enumerate the possibilities for each size cluster, and describe ways to show that some of those representations are the same. The way of writing this down would be like... let's say you have two rings linked to each other)... 0 1 1 0 i.e. ring 1 is linked to ring 2, ring 2 linked to ring 1, neither ring linked to itself. Two rings NOT linked to each other would be represented by 0 0 0 0 A Mobius of 3 rings would look like: 0 1 1 1 0 1 1 1 0 Simple, but when you get to 4 rings, you have to introduce the idea of handedness or clockwise/counter-clockwise intersections or you end up representing two different clusters in the same way. A counter-clockwise intersection would be represented by a -1 instead. And then there's some more stuff about whether this covers orbital/captive weaves (no), tells us whether an array of numbers is physically possible at a given/any AR (no), or whether it says anything about how repeated units of rings connect with each other (again, no). So it would need to be fleshed out more somehow to cover those situations, and (for that matter) multiple ring size weaves. Make more sense in a general kind of way? (Explaining is easier on a full night of sleep.) Sneaking, er, looming suspicion this is veering sharply off-topic :(

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 Posted on Mon Dec 03, 2012 11:27 pm Link to Post: *completely off topic* Good Evening, this is Madeup Reporter with Channel 5 breaking news... We're on location in Chesapeake, VA, where a local womans head has exploded due to maths overload... Her neighbours say she was a quiet woman, kept to herself, and made chainmail. More on this story at 11. Useful Links Site Help: [ BBCode Help | Weave AR/Ring Size Popup | Login Issues | Editing an image in GIMP; so it can be used on the M.A.I.L. site. ] Weave AR Search is back: Try it out!

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Posted on Tue Dec 04, 2012 2:09 pm