Another JPL question (JPL5, JPL7 and so on...)
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Posted on Thu May 21, 2009 7:34 pm
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Thanks Legba! Coif LoL


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Posted on Thu May 21, 2009 8:51 pm
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lorraine wrote:
"The woman done gone crazy."
JPL15!


OK, and NOW write a GOOD tutorial, how to solve the general problem of starting the JPL family of weaves - just to reenter the sanity zone...

-ZiLi-


Maille Code V2.0 T7.1 R5.6 Ep Fper MAl Ws$ Cpbsw$ G0.3-6.4 I1.0-30.0 N28.25 Ps Dacdejst Xagtw S08 Hip

Human societies are like chain mail.
A single link will be worth nothing.
A chain is of use, but will break at the weakest link.
A weak weave will have the need to replace weak links.
A strong weave will survive even with weak links included.
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Posted on Fri May 22, 2009 2:40 pm
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lorraine wrote:
"The woman done gone crazy."

JPL15!


Then crazy be thy name! Great work. I'll have the padded room prepared for you. The nice men with the butterfly nets and the jacket with extra long sleeves are standing by.

Quote:
The higher I go the more the weave twists in a less than attractive way. I think it stops being pretty after JPL9.


That's what I'm seeing about this weave. I made my first strand of JPL5 last night (woo!), and I noticed that while it's a very pretty weave, it's not symmetrical like a pure spiral. I would only imagine that it would become more noticeable at higher numbers.

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Posted on Fri May 22, 2009 6:00 pm
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Lorraine, now that you've gotten all the way through 15, how about going back and doing all of the "Skip" or "Space" variations?


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Posted on Fri May 22, 2009 6:47 pm
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Zlosk, what are those?


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Posted on Fri May 22, 2009 7:25 pm
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Over at TRL, in one of the JPL discussions, someone theorized that variations in JPLn might be possible by rotating the rings more than (360/n) degrees at a time.

http://www.theringlord.org/forum/showthread.php?t=40274

I've got renders of the 6 theoretical variations of JPL7 on the 2nd page of the discussion. Only 4 are physically possible. As far as I am aware, none have ever actually been made.


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Posted on Fri May 22, 2009 8:08 pm
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Wow Zlosk, interesting stuff. Thanks for that link.
When I was trying to wrap my head around JPL but was still under the mistaken impression that it is "just a locked spiral", I made this.



I've been calling it Not JPL7. It makes a really pretty spiral in two colors I think. Do you think it is one of the variations?


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Posted on Tue Dec 27, 2016 4:28 am
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this is an attempt to bring back some of the old members into this discussion. i have some new theory on jpls and i would like to share my findings. since this is possibly the best discussion that i've found, it was important to add here. my assertion is that all jpls (5+) begin the same, not with the formula "# of rings in the starting mobius = (JPLx +1)/2" that has been expressed. now, this is going to be really hard to prove and i think most will have a gut feeling to reject my findings, but please start with an open mind. jpl5 starts with 3 ring mobius, flip 1, add 1. this is proven and accepted knowledge. the shape of that beginning 4 ring unit is what i call "axiom 3 in 1 unit." here is a pic of it:



jpl5 starts like this:



these are all the same "axiom 3 in 1 unit."
lorraine's tutorial for jpl7 starts with this 4 ring unit - mobius 4. a departure from the axiom 3 in 1 unit:



this departure is not huge since the next step is flip 1, add 1. only the first ring is out of place. the rest of the weave ends up working fine. Zlosk worked out the possible variations of jpl7 below. lorraine's jpl7 tutorial gets you the "skip 1" or "skip 6" versions. my JPL7 Alternate weave is the "skip 2" or "skip 5" version. "skip 3" and "skip 4" versions do not work out so well. "skip 2" and "skip 5" versions end up being the most efficient jpl7 because each consecutive ring crosses the previous ring at close to a 90 degree angle. this makes the 2 and 5 version able to have the lowest 6.1ar jpl7 possible. ideal is 6.3ar for a bracelet. the skip 1 and 6 version has rings that end up sticking out farther from the center of the chain.

furthermore, jpls alternate in their "leaning" row's direction. if you follow a repeating ring throughout the chain, it leans one way. if you follow the next repeating ring row next to it, it leans the opposite way. so, if you start with mobius 4 for jpl7, it is impossible to achieve this. if you start with mobius 4 and flip 1, 3 rings are spiraling in one direction. you never see that in any true jpl. so, i'm proposing that all jpls start with the same axiom 3 in 1 unit and then grow to balance the number of rings added. the beginning axiom 3 in 1 unit just needs to be rearranged to be the most efficient for a specific jpl.



the problem described above only gets worse if you start with mobius 5 for jpl9. the larger the mobius, the more rings you end up having out of place. jpl9 will have 4 versions - skip1/8, skip2/7, skip3/6, and skip4/5. skip3/6 and skip2/7 will both be the most efficient jpl9.



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Posted on Tue Dec 27, 2016 12:26 pm
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I appreciate the effort you're putting in to explain the variations to us. Before I just accepted there were variations but now I understand Smile

Btw I make JPL5 without flipping, I just add the rings 1 by 1.

I've now realized I do have AR=6.3 rings, I overlooked them before, so I'm going to give the variation a try.



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Posted on Wed Dec 28, 2016 1:43 am
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what exactly makes Skip 3 and 4 impossible? They look very aesthetic.

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Posted on Wed Dec 28, 2016 2:34 am
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i shouldn't assume, but i think they would require larger ar rings like skip 1/6.



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Posted on Wed Dec 28, 2016 3:10 am
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Zlosk's post implies they're physically impossible though. If they just require higher ARs then I don't see the problem.

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Posted on Wed Dec 28, 2016 3:05 pm
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What a great flashback...thanks mithrilweaver...


"Out of clutter, find simplicity. From discord, find harmony. In the middle of difficulty, find opportunity."
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Posted on Wed Dec 28, 2016 4:25 pm || Last edited by JanPieter on Thu Mar 16, 2017 10:07 am; edited 1 time in total
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JPL7 Skip 3 in 3dsMax. AR=8.0 was the smallest AR I didn't get any intersecting with. I didn't use any coding to find the optimal so it may not be the minimum AR but I assume it's pretty close.





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Posted on Wed Dec 28, 2016 5:54 pm || Last edited by JanPieter on Thu Mar 16, 2017 10:08 am; edited 1 time in total
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JPL5 Skip 2 in 3dsMax with an AR of 6.2.



JPL9 Skip 2 in 3dsMax with an AR of 8.8.





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