"Mad weave is triaxial"

April 2, 2019 4:42 PM

And a triaxial fabric can support cross-stitch representations of symmetry groups that warp-and-weft fabric can't.
posted by clew (43 comments total)

Nobody show this to Cortex, he's already too busy with the stained glass.
posted by Mr.Encyclopedia at 4:51 PM on April 2, 2019 [12 favorites]

I like this a lot. I'm a huge fan of hexagons, in general.
posted by aubilenon at 4:53 PM on April 2, 2019 [5 favorites]

Also speaking as someone who enjoys working with pixel and voxel art I have often found myself frustrated by the fact that "no three points in a square lattice can form an equilateral triangle". I would love to see someone make a game engine that supports sprites with a triaxial pixel arrangement. It would make creating art for isometric games a lot easier.
posted by Mr.Encyclopedia at 4:57 PM on April 2, 2019 [2 favorites]

This is a really fascinating dive into a topic I had virtually no exposure to. Thank you for posting it.

The wikipedia article on wallpaper groups, linked in the article, is also a fascinating read.
posted by gauche at 5:06 PM on April 2, 2019 [5 favorites]

i think it's kind of funny
i think it's kind of sad
the dreams with triaxial symmetry
are the best i've ever had
posted by otherchaz at 5:27 PM on April 2, 2019 [14 favorites]

Is that weave uncommon? I thought it was ubiquitous.
posted by lucidium at 5:28 PM on April 2, 2019

"Wallpaper groups" and indeed "mad weave" are some terrific rabbit holes, let me tell you
posted by panhopticon at 5:30 PM on April 2, 2019

lucidium, it sure looks like one of the common cane-seat weaves to me, but I haven't triple-checked. I think it's fair to call it uncommon in fabric yardage, although there's a ?Raschel knit? `sport lining' that is common.
posted by clew at 5:33 PM on April 2, 2019

Nobody show this to Cortex

When I saw this last week literally the first thing I did was send him this link.
posted by Nelson at 5:36 PM on April 2, 2019 [5 favorites]

> cane-seat weaves

That's what I was picturing! I knew I'd seen it in things like chairs, baskets and rugs, but I couldn't place it.
posted by lucidium at 5:39 PM on April 2, 2019 [1 favorite]

Also speaking as someone who enjoys working with pixel and voxel art I have often found myself frustrated by the fact that "no three points in a square lattice can form an equilateral triangle". I would love to see someone make a game engine that supports sprites with a triaxial pixel arrangement. It would make creating art for isometric games a lot easier.

It extra stinks because converting between hex/triangular coordinates and rectangular ones always ends up with a bunch of irrational numbers all over the dang place. Because your hardware pixels are square, I think it'd be pretty hard to make this look good unless your triangular/hexagonal virtual pixels were freaking enormous.
posted by aubilenon at 5:42 PM on April 2, 2019 [1 favorite]

Here are some very interesting papers on triaxial weaving, and here are some gorgeous (mostly abstract) triaxial tapestries.
posted by ragtag at 5:58 PM on April 2, 2019 [2 favorites]

knitting doesn't handle six-sided symmetry well, either. That's why most 'snowflake' patterns you see are 8 pointed, not 6.
posted by jb at 6:11 PM on April 2, 2019 [3 favorites]

Triaxial weave spread tow carbon fiber fabric, 120g/m2
posted by Mei's lost sandal at 6:35 PM on April 2, 2019 [1 favorite]

It extra stinks because converting between hex/triangular coordinates and rectangular ones always ends up with a bunch of irrational numbers all over the dang place. Because your hardware pixels are square, I think it'd be pretty hard to make this look good unless your triangular/hexagonal virtual pixels were freaking enormous.

Mark Dominus effectively worked out good approximations for different sizes of virtual pixels.

posted by a snickering nuthatch at 7:06 PM on April 2, 2019 [1 favorite]

It looks like only two of the vertices are on integer coordinates though.
posted by aubilenon at 7:14 PM on April 2, 2019

(Also, it's still got 30+ pixels per triangle)
posted by aubilenon at 7:16 PM on April 2, 2019

There are a few other fields that are semi-obsessed with what you can do with hex grids vs. rectangular lattices. One is tabletop gaming, the other is roguelike gaming.

One obvious advantage for both game types and cross stitching is that hex grids have the property of unambiguous adjacency. No nonsense of Moore vs von Neumann neighborhoods, etc.

One day I hope to see more needlepoint roguelike art, I’m sure there must be at least four of us...
posted by SaltySalticid at 7:22 PM on April 2, 2019 [4 favorites]

I haven't actually ever seen a hex roguelike. Can you recommend one?
posted by aubilenon at 7:34 PM on April 2, 2019

Nobody show this to Cortex, he's already too busy with the stained glass.

I was sitting at my table foiling pieces for a biaxial weave-themed stained glass piece when my wife said "hmm, you might like this post...oh hey check out the first comment." So, heh.

Also speaking as someone who enjoys working with pixel and voxel art I have often found myself frustrated by the fact that "no three points in a square lattice can form an equilateral triangle".

It's vexing as heck. I just lumped it and ran with the aspect ratio issue as best I could when I did a cross-stitch Menger sponge a couple years back, but I remember wishing at the time for some kind of triaxial aida to work on. Thought of that again when Nelson messaged me about this stuff the other day.
posted by cortex at 7:44 PM on April 2, 2019 [3 favorites]

I haven't actually ever seen a hex roguelike. Can you recommend one?

Omg, Hoplite. It's the best mobile game ever. You're welcome.
posted by kaibutsu at 7:49 PM on April 2, 2019 [5 favorites]

When I saw this headline, I thought, "Oh, huh, this would interest Mary Shepherd and Susan Goldstine." (mathematical fiber arts is a small world, and we all know each other) Of course, they're both name-checked in the first paragraph, but I certainly hope word gets back to them about this project.

I haven't actually ever seen a hex roguelike. Can you recommend one?

There's a good android puzzle-roguelike called Hoplite.
posted by jackbishop at 7:52 PM on April 2, 2019 [3 favorites]

Seems like you could 3d print a variety of meshes out of flexible TPU.
posted by jenkinsEar at 7:59 PM on April 2, 2019 [1 favorite]

Seems like you could 3d print a variety of meshes out of flexible TPU.

Then you design some great patterns, assemble kits and sell to crafters! fun business idea!
posted by 5_13_23_42_69_666 at 8:27 PM on April 2, 2019 [3 favorites]

Of course, nothing's stopping you building an actual hex grid display.

I'm kinda tempted to do a PCB for an RGB one, now.
posted by automatronic at 9:16 PM on April 2, 2019

Tangentially relevant, I first heard of triaxial weaving from this Strange Loop talk which goes deep into the mathematics of weaving and taught me quite a big.
posted by mad bomber what bombs at midnight at 9:42 PM on April 2, 2019 [2 favorites]

This is such a fantastic find, thanks for posting!
posted by invokeuse at 10:01 PM on April 2, 2019 [1 favorite]

That cross-stitch Menger sponge is very striking.
posted by jamjam at 10:26 PM on April 2, 2019

Hoplite

Oh yeah, I guess I have seen (and enjoyed) a hex roguelike. Sorry for being dumb and forgetting it!
posted by aubilenon at 11:41 PM on April 2, 2019 [1 favorite]

Oooh, old strategy gamer and roleplayer that I am, I love me some hexagons.

Mei's lost sandal, that link seems like it's from a cyberpunk story or something: "Johnny3 pulled out the Yamahari deck, the triaxial weave spread tow carbon fiber of the casing reflecting the neon lights in dizzying patterns".
posted by Harald74 at 12:42 AM on April 3, 2019

Cane weave is based on octagons and squares, but this hex weave uses hexagons and triangles.
posted by bitslayer at 2:54 AM on April 3, 2019 [1 favorite]

The old game Ogre from Steve Jackson Games was one of many titles back then which used hex maps, if I remember correctly.

(Lots of 5”x9” baggies with hex map sheets, cardboard counters, and narrow rulebooks!)
posted by wenestvedt at 3:15 AM on April 3, 2019

Of course, nothing's stopping you building an actual hex grid display.

Has anybody made a higher-density one of those? I.e., a RGB LCD/OLED or e-paper display whose pixels are in a hexagonal grid; perhaps in bezel-less hex tiles that can be assembled into a display of arbitrary size, given the electronics to drive it.
posted by acb at 4:04 AM on April 3, 2019

Another triaxial fabric: Bobbinet tulle.
posted by clawsoon at 5:33 AM on April 3, 2019 [1 favorite]

Oh! Clicking through to this article, the name comes from the Malay "anyam gila", that must be where I've seen it. The British Museum has a nice collection, especially this hot pink pandan leaf basket with twisted star decorations on the lid.
posted by lucidium at 6:27 AM on April 3, 2019 [2 favorites]

Does anyone have a source to buy the fabric (or similar triaxial/mad weave)? A cursory search is turning up only this thread and article. It sounds fun to play with.
posted by fiercecupcake at 7:56 AM on April 3, 2019

Somebody who makes wedding dresses would probably be able to hook you up with bobbinet tulle.
posted by clawsoon at 8:24 AM on April 3, 2019

With all those pieces in place, the last step was very simple: hours upon hours of punishing, tedious manual labour.

lol lol lol.
posted by showbiz_liz at 11:33 AM on April 3, 2019 [2 favorites]

So, is triaxial aida or other cross stitch material a thing one can actually buy? Asking for a friend. I usually prefer to do cross stitch on plastic fabric anyway, so I'm game for any type of material.
posted by tippiedog at 1:47 PM on April 3, 2019

There is triaxial caning, bitslayer, although mass-produced sheet caneweave is all octagonal, afaik. But The Caner's Handbook, for instance, has instructions for two triaxial patterns that interlace true hexagonal caning -- Spider Weave and Star of David patterns.

Caning a wood outline has a lot of freedom compared to modern woven cloth since you pretty much make the outline into a custom loom by drilling holes, and you can drill two rows of holes if you have to. You can inlay suspended solid segments into a hyperbolic plane of caneweave. I mean, people have; I couldn't.

Another english-language source on mad weave: a basketmakers' how-to essays/folios.
posted by clew at 4:22 PM on April 3, 2019

tippiedog, the article makes it sound like the author only got triaxial fabric as a personal sample of really expensive R&D material. But!!! If you're willing to work on plastic, I should think a 3D printer first layer with customized angle and density would work.
posted by clew at 5:12 PM on April 3, 2019 [1 favorite]

Has anybody made a higher-density one of those? I.e., a RGB LCD/OLED or e-paper display whose pixels are in a hexagonal grid; perhaps in bezel-less hex tiles that can be assembled into a display of arbitrary size, given the electronics to drive it.

As far as I can find, no.

I think trying to do custom LCD/OLEDs for this would be prohibitively expensive, but you could do RGB LEDs in a hex grid on a PCB down to about 1mm pitch, and I'm tempted to do it.
posted by automatronic at 2:35 AM on April 4, 2019

Thanks, clew, I was wondering about 3D printed material. I wish someone would print and sell it.
posted by tippiedog at 12:43 PM on April 4, 2019