New family of E4-1 variants
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New family of E4-1 variants
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Posted on Thu Jun 20, 2019 5:33 am || Last edited by EricN on Mon Jun 24, 2019 3:33 am; edited 2 times in total
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I've been playing E4-1 for the past couple months, and I think I've come across a family of basic E4-1 variants that aren't in the database.

Some background: Oops is a sequence of alternating direction European 4 in 1: 45 Degree Seams. The centerline of a regular E4-1 seam is the Oops weave. If one found an angled seam for Oops, what would happen if that were used to zig-zag Oops itself?

Last month I found a seam. Writeup here: Oops (aka E4-1 Unbalanced) 30 degree seam

This is the progression from E4-1 to Oops to my potential new weave:


I've got a couple variations on the weave in the left half of that image, and they all follow these rules, just like E4-1 and Oops do:
    1) All rings have 4 connections
    2) All connections are Euro "through-the-eye" style
    3) The connection diagram (draw a dot for each ring and lines connecting them for each link) is a plain square grid


So am I covering new ground here?

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Posted on Fri Jun 21, 2019 7:17 am
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i think so. i haven't seen anything like this before. i spend some time looking for an oops seam and couldn't get one, so i'm happy to see it can be done.



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Posted on Fri Jun 21, 2019 11:13 am
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This seems to be something new.

From what I can see, the pattern is, on a grain, then pattern [up/down] is [2/2,4/0,2/2,0/4], repeating.


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Posted on Fri Jun 21, 2019 8:26 pm
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E4-1 Variant A:


E4-1 Variant B:


E4-1 Variant C:


I'm pretty sure there are more. I haven't figured out how the whole family works.

There's something important about the 4 rings highlighted in the last image. These three weaves (and also Oops and basic E4-1) are just different tilings of that 4-ring diamond and/or its mirror image. I think it's the real fundamental unit of E4-1

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Posted on Fri Jun 21, 2019 8:40 pm
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Karpeth wrote:
This seems to be something new.

From what I can see, the pattern is, on a grain, then pattern [up/down] is [2/2,4/0,2/2,0/4], repeating.


I was hoping to continue this process to another level, but I'm suspecting it's impossible because that would require a [5/-1] ring.

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Posted on Fri Jun 21, 2019 9:14 pm
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EricN wrote:
Karpeth wrote:
This seems to be something new.

From what I can see, the pattern is, on a grain, then pattern [up/down] is [2/2,4/0,2/2,0/4], repeating.


I was hoping to continue this process to another level, but I'm suspecting it's impossible because that would require a [5/-1] ring.


That’s Why it’s Good to write it out. Wink

I don’t see the logic behind the new ones, what’s the pattern?


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Posted on Fri Jun 21, 2019 10:36 pm
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Karpeth wrote:

That’s Why it’s Good to write it out. Wink

I don’t see the logic behind the new ones, what’s the pattern?


Oops is E4-1 that goes up-down-up-down, but it doesn't have to change direction every column to maintain 4-in-1. There's UUDUUD... (Josue Sheet), UUDDUUDD...(Secret), and probably several more before it just looks like E4-1 with fault lines. They are still all the same family and basic construction.

I think this is what's going on with my variants. I'm building a similar family of weaves by zigzagging Oops in different ways.

There's also Gridlock-style transforms that maintain 4-in-1. Variant-A might involve one of those.

I'm also trying create a sensible, cohesive naming scheme for all of these.

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Posted on Sat Jun 22, 2019 12:24 pm
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I can’t say that I’ve seen this before either, but I still haven’t fully explored all known European sheeting techniques. This is excellent information.


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Posted on Sun Jun 23, 2019 9:39 pm
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I stared at variant B and thought, ”This is not infinitely repeating, This is bands bolted together.”

Then I realized; the ”true weave” form should be ”B, E4 reverse B,E4”, instead of ”B, E4, E4, B”, - that would remove the bolted feel.


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Posted on Mon Jun 24, 2019 3:30 am
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Karpeth wrote:
Then I realized; the ”true weave” form should be ”B, E4 reverse B,E4”, instead of ”B, E4, E4, B”, - that would remove the bolted feel.


I need to think through this description more. I'm not visualizing it.

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Posted on Mon Jun 24, 2019 9:35 am
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EricN wrote:
Karpeth wrote:
Then I realized; the ”true weave” form should be ”B, E4 reverse B,E4”, instead of ”B, E4, E4, B”, - that would remove the bolted feel.


I need to think through this description more. I'm not visualizing it.


What I call E4, E4 are the grains of rings connected in a classical E4-1 fashion; in the Middle of the picture, a row of [2/2] connects to a row of [2/2], which in My eyes look more bolted and not continous. B is made of a row of [0/4], a row of [4/0], and Two rows of [2/2]. My suggestion is instead of [0/4][4/0][2/2][2/2], it should just be [0/4][4/0][2/2]. This reverse the lean on all the rows, making a sequence of [0/4][4/0][2/2][0/4][4/0][2/2] the smallest to be able to connect back to itself.


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Posted on Mon Jun 24, 2019 2:25 pm
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Got it. I'll try to make that. Eyeballing it, there might be some collisions at this AR.

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