Origami Projects

I've always been mildly fascinated by origami, although I tend to like very clean, crisp-edged shapes that aren't overly ornamented. As I gain more practice, I may change my opinion. I learned a few simple shapes when I was small, but it's apparently taken with a vengeance after lying dormant for decades. This is a pattern that I found online and wanted to attempt, the first in a long time aside from the ubiquitous cranes. The accordion folds were ... challenging, to say the least. It's a bit stretched out of shape, unfortunately.

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I'm quite proud of this one since I invented it. I had been making cranes at work and two things happened at the same time: I got bored of them, and one of the women at work put one in the flowers on her desk and called it a hummingbird. I decided that I would try to make a hummingbird for her.

Well, the one hummingbird diagram that I found online was ... underwhelming. Boxy and clumsy, unlike the lithe, agile little creatures it was intended to mimic. I had already altered the typical crane pattern a bit to make it more to my liking: I'd folded the head and tail a bit asymmetrically so that the wings folded up and forward, making the bird look a little more active and less rigidly symmetrical. A little fiddling with that altered crane, and the following hummingbird was the result. A rather casual and not-at-all formally stated diagram is also available.

I've also taken to making these smaller and smaller. The 6" paper makes a bird that is close to the size of the real animal. The 3" paper makes a bird that's pefect for filling a glass goblet on one's desk at work. :-) The 2" paper makes a bird that's guaranteed to blow people's minds. They also hang well from string and would decorate a Christmas tree very nicely.

I hope to continue inventing diagrams; it's much more fun than just folding something someone else came up with.

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A delightful shape. I'm fond of modular origami; I find it mathematically appealing. This is yet another cube, made with something other than the everpresent Sonobe module. It's pleasantly off-kilter, and when made with 6" paper, surprisingly rigid and robust.

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Much more annoying diagram. It works well enough, but doesn't have that seated feeling that the other cube's modules have. Pretty, though. There is probably a way to really snazz up the center, especially with foil paper.

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One of the first patterns I learned when I was a kid was a hooded sparrow of some sort. I remember being intensely frustrated with it because, unless it was held firmly by the middle, its legs spread apart. The thing simply wouldn't hold its shape without being held. (This is one of the reasons why I'm so pleased with the hummingbird that I invented. It holds its own shape.) This peacock, while delightful, has the same problem. It's not as bad as that old hooded sparrow, and I think foil paper would probably make a big difference.

This is not quite standard origami, because it uses a 2x1 sheet of paper. I'm mostly a purist; I like the challenge of seeing just what can be accomplished with a single uncut square. The things people can do often amaze me --insects with six appendanges, for example, from an object with fourfold symmetry -- and I like the idea of investigating just how far you can push a simple square. There's also a simplicity that I like, probably the same reason why I dislike cutting steeked sweaters (see the knitting page). It's just mathematically ... unattractive.

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I include this here only for completeness. I was mucking around trying to remember how to make a dahlia, and while I didn't manage it, I did make something interesting yet useless.

What? Consult the diagram? That's cheating!

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Don't breathe. Don't look at it -- it might fall apart. Putting this together, out of 2" papers, was one of the more frustrating things I've done. It's sitting on my computer desk at the moment, and I can probably use it as an earthquake detector. The second any of those damned little flaps pop out, I know something tectonic has happened -- or a truck has driven past outside.

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Years ago, I saw a sonobe-like cube made of these modules. It's not a sonobe module, but it fits together in a very similar way, so it's definitely sonobe-like. On the faces of the modules are two leaf-shapes.

Well, for years, I kept one of these modules (can't for the life of me recall how I came to have it or what happened to the other -- presumably -- five of them) and didn't do anything with it. Then on 4DEC06, I was in need of a distraction, and finally took the thing apart ... barely ... to see how it went together. It was deceptively complex, actually, but I managed it and then promptly made cube 1. After that, I folded part of the module the other way and made cube 2. Still working on ways to engineer color changes on the thing.

As with all sonobe-like modules, you can make dodecahedrons etc. with these things, but while they are similar to sonobe modules, the flaps are juuuuuuuuust a titch smaller and hence a bit more of a pain to assemble. They stay together fairly well, but not quite as robustly as a standard sonobe module or a biggish chaos cube. Diagram probably not forthcoming, as completing one of these modules is still in the realm of "jiggle until it fits" for me. Once I do manage to straighten it out in a more rigorous fashion, I'll put up a diagram.

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Gorgeous! More modular, of course -- I found this one online on LJ; the smallest model that the folder had made was out of 3" papers, and all I had available was 2" papers, so ...

Problem -- the 2" paper is small enough that curling back the leaves isn't so easy, so I haven't done it yet. A bummer, since the interior of the leaves is very prettily patterned. I really need to get some 3" paper to keep around the apartment so I don't have to either try new folding diagrams with enormous or cheap paper, or else 2" stuff.

Pattern can be found online.

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Made of larger paper and hence the leaves could be curled, but it was also made with rather substandard paper, unfortunately. One of those "page a day" calendars that is nice enough, but uses glossy, magazine-style papers that aren't quite square. Oh, well. It certainly turned out well enough, and illustrated the similarity of dodecahedra and icosahedra rather nicely as well.

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When I made the 30 modules for the above piece I ... well, I made them in a universe where 36 == 30. Had a few leftovers and played around with them a bit.

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These things never get old, do they? My first exposure to modular origami was the venerable Sonobe module, nearly fifteen years ago, I think. Same so-so paper as above. Nothing really fancy here, just really a run-of-the-mill sonobe. Note the isomorphism between this and the full arabesque.

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I adore this one. Adore it to bits. I love cute little tesselations like this and am really starting to nurse a love for tesselations in general. I think between this and modular, I may never fold another bird base again. (Well, okay ... )

This pattern can also be found online, and I am dying to try this one out with smaller paper. The model below was folded from ... oh, hell. Larger than 6" paper, at least. 8"? I can't recall. It really isn't a hard one; the initial collapse is much simpler than I first thought. No weird rotating like with the Kawasaki rose. This one really does go together very quickly.

Views 3 and 4 are of a model folded with 6" paper, with a rather obnoxious pink moire pattern on the back. It looks quite nice with the butterflies folded in white on the paper, though. A pattern like this in blue and green might be pretty, like butterflies on water. The smaller model is shown sitting on top of an unfolded piece of 6" paper to give you an idea of starting and finished sizes and what sort of shrinkage you can expect. This fellow on LJ folded a model from a 1.5" square of paper that ended up the size of a penny. Isn't it wonderful?

Okay, so I had 3" and 2" paper on hand. View 5 demonstrates two things: 1) I am out of my mind. 2) It's an illness, really.

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I tried quite a few versions of this before arriving at this one where I achieved a full and infinitely extendable tesselation. This is a marvelous, gorgeous little piece of work -- in its half-collapsed state, it looks fantastic with all these little crystalline structures emerging out of a flat piece of paper. It's also very satisfying -- and I jumped up and down when I investigated it further and found that the man who invented this (Shuzo Fujimoto) also did a full tesselation!

I was also looking at his Hydrangea, but that seems for some reason to be less attractive to me. I've messed with it and made a few modular cubes using it as a starting point, so I'll have to take some good, well-focused pictures of those and then upload them. I really need a much better digital camera in order to do that, though.

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Oh, this one is wonderful! I can't wait to try it with some colorwashed lavendar paper, because it's really going to be a showstopper. I love the fact that it's modular, it's an action model, it's simple, and it's magnificently clever. This model really combines all the best about origami and what makes it so compelling to me. A genius creation.

This one was made out of the not-too-fantastic glossy-magazine like paper that is included in those page-a-day origami calendars, the same paper I used for a few of those sonobe-like things up above. This sort of paper, slightly but noticeably off-square, is dismal for involved folds, but fine for sonobe-like modulars. Here however, you can see the printing on the inside of the petals. Oh, Well. Still lovely.

Ideally, this paper would be fuschia-red on one side and yellow on the other, so you could make a rose with the reddish side facing out for the petals, and the yellow inside -- like those roses the petals for which turn red where exposed to sunlight.

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And another for my roommate, who likes yellow roses. You can see that these also make excellent cat toys, but few smallish things that aren't nailed down don't -- at least in my cat's highly biased opinion. My roommate stated that the closed cube was a rose in "stealth mode." :-)

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Okay, be patient. I can't for the life of me think of a good name for this. It looks quite nice in "person," much more dimensional since the four spread-squash folds are also interlaced with four smaller ones. I made this out of the first-level collapse of Fujimoto's "Hydrangea," which is also the central collapse of the "Crowding Butterflies" above. I was messing with it for a bit and then realized that I could make it behave in a sonobe-like fashion. After hyperventilating, I calmly made five more and discovered that indeed I could.

The two best types of origami -- modular and tesselations -- together! Hopefully better images and diagrams will follow.

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Again, be patient. I made this one from ... sort of the start of a "Hydrangea" tesselation, but not really. With this one, there are only those four spread-squash folds, which means you can flatten them completely. The corners don't meet up as neatly as with the previous one, which means that you can see inside the cube. As this means you can also see the unused flaps in the interior, it probably needs to be neatened up a bit before it's hauled into prime time, but once again, I'm just thrilled to have come up with my own semi-tesselated (well, tess-inspired), modular pattern.

The views are of one made with 3" paper, and one made with 2" paper. Note to readers: unless you like impossibly fiddly origami, do not make something that requires four tiny spread-squash folds out of 2" paper. My eyes are still rolling.

I should note that both this and the previous cube are wonderful for experimenting with patterned paper. I wouldn't use patterned paper with the majority of the patterning on the corners, though. Try to get papers that are either mostly patterned in the center, or that have something on the corners that is also repeated elsewhere so you don't mind losing it.

Pattern here.

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Unless you wanted to make a bird with 32 feet and a giant ass, I can't see that this would be a terribly practical base. It probably has few real applications or uses, but it's quite interesting. Unsurprisingly, I made the pink one first, and then wondered how much further I could push it. That resulted in the two white ones. (The small white one with the yellow line on it is a standard bird base, on the smallish side.)

This really is quite a fascinating little diagram. As the 3rd level one is not appreciably smaller than the 2nd level one, I have a suspicion that the piece has a fractional dimension, and if the pattern were recapitulated an infinite number of times, it would use a piece of paper with finite area. I'm not certain, but it does seem to be the case with a little thought.

Also, the paper for the 2nd and 3rd level ones (the white ones) must have small corner pieces removed from it, and I suspect that a 4th level would require the removal of other pieces as well. This is unsatisfying as it means that the diagram cannot be made with a single uncut square, but I haven't determined the infinite limit of the piece required to recapitulate the pattern an infinite number of times; that may indeed be a square, but I doubt it. At any rate, I suspect that many more levels would cause the paper to go a bit "Sierpinski" on you.

The collapse needed to create the final bird-base-shaped piece is remarkably non-annoying considering the fiddliness of the folding. This is really quite charming and very pleasant as diagrams go. My roommate suggested that the 1st level one (the pink one, and I'm counting the small white one as a 0th level one) would be useful if you wanted to do an octopus.

I posted about this on the LJ Origami community, and was promptly sent to this magnificent thing, which shows exactly what the shape is for an infinitely recapitulated fractal bird base! (The pattern doesn't show the slits that need to be torn, though, so beware if you want to try this.) Darren was kind enough to run it through a program he has and demonstrate that the infinite limit does indeed converge on a finite area and the shape that my own preliminary ripping and fiddling seemed to indicate. I'd encourage you to visit and dig through his site. His other things look quite wonderful.

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