Locks

At the AEP convention in Leon, Spain, earlier this month, I asked Miyuki Kawamura, the young Japanese rising star of modulars, the following question: How many types of lock are there in origami? Her answer: Hundreds. --Well, but in broad categories? --Maybe, twenty. 

Someone should publish a running list of lock types, with little sketches or photos. This would be an open database that anyone could later add to. It would not make that person money or much prestige but it would be incredibly useful for all of us in origami, for all sorts of reasons. 

I am not a modularist, but merely gaze on the field from a respectful distance. Yet even for us single-sheeters locks are important, and it is clear that modulars is where the subject is explored most thoroughly and directly. It has to be. 

I work on faces and much of the work tries to keep the sheet flat or nearly so, but sooner or later one wants to bend the sheet around and then the question is, how do you join the edges in back. 

Three-dimensional animal origami, which is all the rage nowadays, and rightly so, obviously also faces the same problem. Invariably there is a seam line, under or in back of the model. This is a consequence, almost mathematical, of the fact that the paper starts out with edges; and when you work flat, edges, though probably different ones, stay present every step of the way. You come to the end and still have them. If you started out with a tube you might have less of this problem, and with a sphere possibly not at all (nature’s clearest origami is indeed spherical--there is a blastula: it gastrulates), though even with these the problem of locking flaps exists. Also, such rounded forms are harder to work with: we actually need those edges of the flat sheet pretty badly. 

One has to admit, the sort of thinking that comes to the end of a process and asks ‘now what’, finding itself stuck with a problem it should have known all along it would encounter, is pretty defective. Though that’s the state a lot of us are still mired in. Komatsu in his owl, Diaz in his polyhedral/volume studies, and Joseph Wu in some of his 3D work have made efforts to carry us a little beyond this primitive condition. 

In any case locks are interesting, I want to say “satisfying”, all by themselves, quite apart from any pragmatic function they may serve in hiding ugly seam lines and as a replacement for glue. There’s a distinct pleasure when a flap fits into a slot and ties a form nicely together; when all the messy sliding about gets brought under single control; when all degrees of freedom suddenly disappear. --And it is origami’s job to study what is satisfying. 

So how about it, Miyuki? It would take you all of five minutes. (OK, five hours.) 

Saadya

Another bird---

Just seeing if I can't incorporate lessons from ‘technical origami’, here in the form of point-split feet, within the overall simpler, streamlined language that I still believe is more appropriate for birds in origami.

This model is under 30 steps long.

From a weird variation of the Preliminary Fold, which instead of dividing the center into 8 x 45 degrees, divides it into 12 x 30 degrees. More on this later.

S.

Concentric Circles

[Revised January 2010] There are lots of ways to get a sheet of paper to fold up nicely. Here is one way I would never have come up myself: that is, if I hadn't tried to copy somebody else's work. I failed (at first), but came up with a different interesting something which seems not to have been remarked on before.

The work in question was the piece of David Huffman's shown by the Institute for Figuring, who mistakenly label it a “Tower of Concentric Circles” -- when (a) it is not a tower and (b) Huffman has another model which is (!).  I imagined at first that this was simply a cone with concentric mountain-valley reverses, which is what I tried to make. You can see from the Huffman photograph that the cone-tip is twisting its orientation as it moves toward the center, which wouldn't happen with concentric-circle folds around a cone's apex, but I explained this to myself as either a trick of lighting or as some flexibility in the form that allows it to be bent that way post-folding (no such flexibility exists as it turns out).

My correct subsequent reconstruction of Huffman appears here. The rest of this article (except the final paragraph) proceeds as originally written.

* * *

Some tentative remarks on the Huffman piece recently appeared in Erik &Marty Demaine’s "history of curved origami sculpture". At least as of this writing, the Demaines neglect to mention a rather striking feature of such concentric circle patterns, the fact that you can do THIS:






Nice, no?

The math here is pretty straightforward. Think how if you have a disk with a radius cut, you can make a cone of it by tucking one cut edge under the other, and then sharpen the cone continuously by twirling the cut edge underneath. Now notice that the same reasoning applies also to all horizontal slices of the cone (=concentric circles on the disk), which can be made into mountain & valley folds. It’s a neat illustration of several kinds of symmetry, and a way of folding a sheet into a quite small shape that does not involve any straight folds. --How small? Mathematically you could wind the thing up forever, but physics as usual gets in the way: here in the form of the thickness of the paper, which causes the surfaces at some point to stick.

[Note, 2010: This is my "Concentric Winder." I have a few new thoughts about it, which I'll put in a separate Blog article.]

So far as I can imagine, this trick will work smoothly ONLY with concentric circles (though there is one other spiral form which almost works too, albeit with surfaces not exactly flush to each other). The mountain-valley pairs need not be equally spaced, but they do need to be circular and to have a common center. So, I will hazard the claim that this seems to be a means of compacting paper that is unique to sheets curved-folded by means of concentric circular folds.


Now, leaving Huffman aside, with this very same model you can also explore a different property of concentrics: the one that the Demaines are interested in, following work pursued early in the 20th century by Josef Albers with his design students in the Bauhaus, and later in the century by Thoki Yenn and Kunohiko Kasahara in the origami world.

Notice that when the form is wound up--with more than, say, one quarter of the circumference tucked under itself--the ridges of the mountain & valley folds add to the stability of the disk, which is flat on average. That is the familiar corrugation effect coming into play, the same method that gives the added stability to wavy plastic rooftops and corrugated cardboard.

When you unwind it though, a strange thing happens. The corrugations weaken---that is not itself surprising, as the mountains/valleys are growing shallower. But long before the disk becomes altogether flat, the surface will have LESS stability than a comparable disk without the mountain and valley folds. In fact, the disk starts to look for any excuse to break out of the plane: it refuses to stay flat! By the time the disk is unwound completely, it will naturally assume a contorted, saddle-like shape.

Why is that? Notice that the mountain and valley folds add some springiness to the paper, pulling the edges, and indeed every part of the interior, closer to the center. That means the circumference now has to occupy the same space as a smaller circle. It can’t do that while remaining in the plane, so it bulges out of it. The same reasoning applies to each of the smaller circles, so you get a nice uniform twisty shape that is saddle-like.

Why it's always 2 up, 2 down, and not some other number, remains a mystery to me.

Saadya Sternberg

Llopio’s Moment of Truth

This model with all its drama and flourish was designed by Neal Elias in the 1960s in the USA, and folded expertly a few years ago by Eyal Reuveni, here in Israel.

Full of suspense, presence and equipoise, it is the only ‘dated’ work I included in the Tikotin Museum exhibition, besides the Yoshizawas. But it not only holds its own against the four decades of advances in origami technique that came after it, it even remains distinct, like an island jutting from the sea. It’s kept its innocence too. Though it points in the direction of technical origami, this creation by the pioneer of box-pleating manages to avoid most of the clunkiness to which that technique is prone in lesser hands. It is not "showily technical", does just enough to get the job done, and so holds a quiet strength.

Elias was also the pioneer of the joined two-object model, and of course of the significant color change. I’ve noted elsewhere that having two objects of equal weight in a sculpture turns it from being a noun phrase (‘this is an A’) into a verb phrase (‘A is doing Y to B’). With two linked objects, besides an implied action or relation the viewer can shift his self-identification from one object to the other and thus invert the inflection of the verb. That may be part of the fascination. Here in origami the dramatic possibilities are still more pronounced: when everything is formed from a single sheet of paper, you perceive what the sculpture is meant to be, notice its different parts, and sense the fateful continuity between them, all in the same quick flash of recognition.

One does not need to have Spanish blood, or to have seen it shed in the bullring, to appreciate the drama of this moment. For this is what the viewers have come to see: the ‘Minotaur moment’, when matador and bull, before one of them cedes its life, suddenly become one. How perfectly this union of souls is expressed here, with matador and bull made of the same stuff and the same color: separated only by the sheet that joins them, with its metaphysical union and two-sidedness. (As in that beautiful English word which also means its opposite: to cleave, which is both to cut and to cling--both scissors and glue--and which term presumably derives from leaf, the primordial sheet.)

It pleases me to think that this old work on a Spanish theme might give courage today to folders in far-off places: to people in sunny or southern climes, in Spain itself perhaps, or in South America, or even southern Africa. Some place locked within fields and mountains, where news of the world does not fast filter in. For if one is dismayed by how much is made of technical origami in the various media today, it is good to remember what paperfolding once was, and still is, about: Firmness of purpose in the cleanness of line; purity of soul in the expanse of clean surface; whimsy and lightness, as in the dexterous grace of the knife-thrower: the joys, conjoined, of intelligence, simplicity and magic.

at the Tikotin Museum of Japanese Art.

Three Tenors

A homage of sorts to Carlos Corda.

S.

"Japanese Art"

I’ve been spending so many hours lately in the company of some great Japanese and Asian Art--for example, the okubi-e prints of Kitagawa Utamaro. It would be strange if nothing whatsoever of that rubbed off on me.... Here are a few things where the influence has, hopefully, been favorable. --I post them with some hesitation, for clearly there is still a long way to go.

These are all variations on a theme, wet-folded from paper of various kinds. Actually, I’ve been wanting for some time to branch away from foil-paper folding, my main medium for face-work. Foil-paper is a beautiful & rich medium unto itself, which is either a department of or a field adjacent to origami; but there are certain paperfolding values that foil manipulation just can’t capture. And in any case it was high time I learned how to wet-fold.

More is coming.

I’ve held off doing figures that are viewable 360 x 360, not because that is not a desirable result in itself, but because I wanted first to be sure I have a technique which preserved clean surfaces in the face, so that it would not invariably be grimacing, grotesque or “fantasy-oriented” as it is with some of the others who work onhuman figures. Now that I have such a method I can proceed to the rear and work down to the rest of the body, if need be. But I am in no hurry to get there. As I see it, the technical problem to be solved is not how to go all the way round or get all the way to the toenails. It is how to assure that each step does not “injure the paper”, to adapt a quaint concept from Yoshizawa.

The last few works are less “Japanesey” but still perhaps “Asian”: I may have had in the back of my mind (I certainly wasn't directly copying anything) some Tang Dynasty sculptures with the clump on the top of the head and that beautiful air of disarming tranquility, that you can make with a dollop of clay. That is possible with origami too. And since it is possible---it is necessary.


Saadya

Smell of a Bird Base

Been having trouble lately with my Birds. Partly this is nature’s fault: Many birds have at least three colors, rather than two: a topfeather color, an underbelly off-white, and red or brown for foot & beak. That’s not even counting the black of the eye. With origami you’ve got two basic colors to work with plus a pseudo-grey from shadow-pockets—not quite enough for this particular job.

One could, I suppose, bite the bullet, and add another sheet with one or two new colors. Joseph Wu has gone in this direction with his elegantly-marked Frigate Bird. And I seem to remember Nicolas Terry doing something similar to get a multicolored frog.

An option for those of us stuck, religiously, with single-sheet color-faithful origami is to confine ourselves to those birds that do follow a 2-color scheme. Pigeons, for instance, which run the gamut of gray-scales and blended patterns, sometimes come in an all-gray or all white body plus reddish feet. Likewise there are quite a few avian species in which the females, who tend to be interested in crypsis rather than showiness, keep their color-numbers to an origami-manageable minimum. (There are, of course, always reasons why an animal has the color numbers it has.)

Another problem is idiosyncratic---or maybe just personally idiotic. A long time ago (20 years… sheesh!) I convinced myself that a standing bird is fundamentally a four-pointed creature, from which it follows that it should be designable from a bird base (5 points: hide one). If you want to use the fancy techniques that have since come on line, to add complexity or detail---open a beak, pry apart toenails, start the wings a-flutterin---this ought to be doable optionally at the last minute, modifying extremities to taste, rather than by designing complexity in from the outset or inventing new bases as I believe Roman Diaz once argued is necessary. All the above poses a certain challenge, since to date I have not been able to pull this off entirely successfully.... Roman in a recent letter even claimed that “The smell of a bird base is difficult to disguise on a model.” But what to do? I happen to like the smell of a bird base.

So here's where we are, on a cold November night.

Curved Folding, revisited

Work in progress. (i.e., I haven’t ruined it yet.)

The aim and method is the same: the minimization of lines; the exploration of the inherent softness there is in smooth paper surfaces joined by curves and open folds. I think in the end paper has more possibility for expressing tenderness, or at least receptivity, than even skin on flesh, nature’s original. But for that one needs to get away from the angularity of most origami.

It’s been about a year since I’ve done anything new in this direction. I guess we all have stages where that keening high origami brings, fades of itself or is forcibly set aside. I have Joseph Wu to thank with his invitation to exhibit at Vancouver's Pendulum Gallery (in tandem with PCOC 2007) for getting me jump-started: What I sent him may have been older material, or things derived from older ideas, but the juices now seem to be flowing. I doubt that anything less than the knowledge that people like Joseph and Michael LaFosse and possibly Roman Diaz will be there (among other luminaries) to see those things and harrumph at them, could have got me going---

Cheers!

Saadya

Mother and Child

I was very glad to get Giang Dinh’s “Mother and Child” for the Tikotin show, and glad too, that by independent decision this image appears on the catalog’s front cover and on the invitation card. For it nicely represents the guiding thought of this exhibition: that origami can sometimes be an art, as high as any of the traditional arts. Mere modesty & self-restraint keep me from saying there are even heights of artistic expression which origami can reach that are not possible in other media of sculpture. (Of course origami has its limitations too.)

If one asks what those are, here—what makes this work art and great art at that—there are some obvious points to start with. Immediately noticeable are the clean modern lines, the long curves and fluid surfaces. Also the work has a manifest simplicity: while there are certainly areas where it is not easy to guess how the thing is folded, the bulk of it, and the main inversion at the bottom, is perfectly obvious and followable by the eye; there are no tricks, what is achieved is achieved without technical sophistication, which is unnecessary and has no place here. Then too, there is a concept expressed: the shy child peering out of its mother’s protective skirts. This is not one of the common variants of the mother & child theme in sculpture, but is closely enough related to them, and on reflection is better expressed in folded paper and in this form of fold than it would be in pretty much any other way. The genetic relation between the figures is signaled both by a repetition of form and the physical continuity of the paper, simple but deep ideas that everyone recognizes with instant delight.

In the dim recesses of history out of which origami sprang, 800, 1,000, 1,200 years ago—in the rituals of the Shinto religion—paper, white paper, was associated with purification; and folded (and cut) ceremonial representations of humans and deities began to emerge, with folded animals soon to follow. This figural work of Giang Dinh’s has an aspect of purification too, in its whiteness and smooth contours.  It is also religious in its way, though the religion seems more a sort of Christianity; there is the protective mother and child theme itself; and the innocence of the child expressed in its shyness; and the drama of the vaguely nun-like robes. That drama and the odd externality of it—mystery expressed through concealment, enrobement; individuality scaled back to just a face and a gesture—also has associations with the traditional stage performances of Southeast Asia, a fact far more explicit in the other installation by Giang Dinh in this show, his series “The Dance”. But it is “Mother and Child” which brings together tradition with modernity, ideas of origin and purity and innocence with replication and continuity, and a new fusion of East and West in a single lithe, iconic package. I take my hat off.

Fleeting Life

[Added 2011. Visitors from theequinest: Roman Diaz sent in these fantastic horses for the Tikotin exhibit, with sequence numbers stuck in each; I arranged them as best I could, chose the name "Wild Horses" for the whole installation, and took the photograph. Diagrams for Roman's Horse are in his book "Origami for Interpreters". I dabble in this theme too, and you might like my Equestrians,  other origami horses (scroll to bottom), or these Horse Heads.] Diagrams for my Horse may be found in my book, "Sculptural Origami".]

At the very last minute that it was possible before the Tikotin opening, Herman Mariano handed me this fine “Kiwi”, designed by Roman Diaz, that he had finished the night before. --At 81, Mariano shows no signs of slowing down. For this Kiwi he used a coloration technique that is new to him: applying dry pastel to the flat sheet, muffing it around with cotton then spraying on fixatif. (Paul Jackson has already been doing this for several decades: as far as I can tell from looking at his things, Jackson applies one or two pastel colors to a reflattened sheet AFTER precreases have been made so that fold lines will pick up extra color). –Pastel is about the only application that can actually augment the ashy dry paperiness of paper while coloring it, keeping surfaces lively, fragile and translucent: all other color treatments tend to make a sheet seem heavier, shinier or more opaque. More, in fact, like the traditional deadening materials of metal, wood or stone.

An odd, possibly unintended consequence of that treatment here is that the beak of this Kiwi looks a little like bone, more so than keratin (which is in fact denser and shinier than bone). Now, we already know that Diaz has studied the difference between representing animal bones in origami and representing animal flesh: there’s his humorous (why?) "Cow’s Skull", which is unmistakably skeletal rather than fleshy; and in his recent "Wild Horses", something was done to the shape of the heads that makes them look vaguely bonelike, as an animal straining to run slightly does—pushing or pulling against death. Somehow or other this effect has transposed itself onto this innocent Kiwi, half-living, half-already-extinct-fossil, in this interpretation of Diaz by Mariano.

Opening

Recovering slowly from the opening of the Tikotin show... According to the Museum’s final count, 594 people packed themselves into the exhibition halls in the two hours of the opening on mid-day Friday; I’m told they haven’t seen such crowds in many years.

All of this initial success can be credited neither to the quality of the show (which no one knew about beforehand) nor to the publicity (which was pretty slight). Rather there must be a great pent-up curiosity in the public about origami. Now however that the exhibit's been seen I expect the numbers only to climb as word of mouth spreads.

The dignitaries came too, of course, and warmly congratulated each other. I was moved however to hear Tikotin's daughter Ilana tell about that funny little man, Yoshizawa, who would come to their home in Japan, and who would never stop folding.


The night before the opening I went round & counted how many discrete objects there were (a herd of horses counts as six objects, a work of modular origami as one). My total came to 162. The number of “installations” or “sensible groupings” (a herd is one object, a pair of birds another)--which is more subjective--varies between 60 and 100.

Here is a very modest sampling. Click on the images for a higher-res view.

Saadya


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"Treasures of Origami Art", works by 25 world-leading origami artists, showing now through the end of the year at the Tikotin Museum of Japanese Art, 89 Hanassi Avenue, Haifa, Israel. Please call the Museum for hours: 04-838-3554.
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Robert Lang's Cervids



Linda Mihara's Connected Crane Quilt



Yoshizawa main table


Yoshizawa Swan family


Top: Giang Dinh's fine wet-folded series, "The Dance". Below it is Yoshizawa's Elephant, one of the works that was in the original 1955 Amsterdam exhibit arranged with the help of Felix Tikotin.



Ron Koh Goldfish


Tomoko Fuse Tessellations


Fuse Modulars folded by Fuse acolyte Rosana Shapiro



Ray Schamp's "Corrugations" wall


Tomohiro Tachi's Teapot


A tessellations table (one of three featuring Eric Gjerde, Christine Edison, Christiane Bettens and Joel Cooper)


Old Goat


LaFosse Butterfly


Some things of my own

Tikotin Exhibit--first images

I've been enormously busy with this show, the opening is the day after tomorrow... But I have to say it looks magnificent. Here are just a few "teaser shots". --More to come


Saadya



Exterior with "cranes"


Main display case--Elephant at center is Yoshizawa's


Joel Cooper's "Cyrus"



Y penguins from the 1930s


Roman Diaz' "Wild Horses"







View of Haifa Bay from promenade back of Museum