Friday, November 16, 2007

"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.


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.

Wednesday, October 24, 2007

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---



Monday, September 10, 2007

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 show: 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 why that is, 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 one 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. And 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 work 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.

Wednesday, August 29, 2007

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.

Saturday, August 18, 2007


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.


"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.

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

Wednesday, August 15, 2007

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


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

Wednesday, July 18, 2007

Camel in the Knesset

This camel is on display now at the Knesset, to help Israel's parliamentarians think this week as they mull over conditions for its Bedouin population.


Wednesday, July 11, 2007

Flitting Bird

Designed 1987; new treatment for the head--last night.


Thursday, June 28, 2007


. . . . .

What is it men in women do require
The lineaments of Gratified Desire.
What is it women do in men require
The lineaments of Gratified Desire.

-- Wm Blake

Great old word that, lineaments, no longer much in use. An outline hinted at, is how we would put it today—except that outline suggests too much of contour and silhouette, not enough of the body lines. Lineaments: the lines, the main structure, the suggestion of it, the indication and idea of it, projectable from the surface, leaving aside almost the body itself, the skin and bones and flesh and motion and the very soul—all there but abstracted.

What besides origami accomplishes this, hovers so precisely between idea and entity? Intelligence not quite incarnate, still hinting, suggesting, but obeying for all that its own strict laws.

. . . . .

Saturday, June 23, 2007

Treasures at the Tikotin

I am thrilled to announce here that beginning August 17, and running through the end of the year 2007, there will be a large museum exhibition of artistic origami in my country.

The exhibit, “Treasures of Origami Art” will be shown at the “Tikotin Museum of Japanese Art”, in the scenic port city of Haifa, Israel. The Tikotin houses the most significant collection of Japanese and Asian art in this part of the world.

The show’s theme is the emergence of origami into a full-fledged sculptural art. About 100 origami installations will be in it, representing works by some 25 artists and designers from 10 countries. These include: Akira Yoshizawa, Robert Lang, Tomoko Fuse, David Brill, Michael LaFosse, Joseph Wu, Roman Diaz, Brian Chan, Linda Mihara, Giang Dinh, Tomohiro Tachi, Joel Cooper, Ronald Koh, Arnold Tubis, Nguyen Hung Cuong, Saadya, Eric Gjerde, Christine Edison, Ray Schamp, Christiane Bettens, Fernando Gilgado, Bernie Peyton and Xander Arena.

There will of course be expert workshops, large-scale origami and various “publicity stunt” events held in tandem with the show.

I’ve been working intensively on this project for the last 8 months, and on and off for several years now. Stay tuned for more information in the various media soon.

Hope you can come!


Wet Folds

I’ve been asked more than once by people who see my curved things: do you wet the paper? And occasionally: do you press the paper into a mold?

The answer to both questions is of course no. And as to wetting the paper, I don’t often practice wet folding (though a bit more so of late) but instead like to glue the paper to a stiff aluminum foil before starting out.

But it took me a while to understand what people were really asking here; and also to realize that even some of those who have heard of wet-folding may have a mistaken idea of what it entails.

People think when they see a curving surface (especially one curved in two directions), that since paper in its natural state is flat, its surface properties must have somehow been altered: that the paper has in fact been stretched. And they think that moistening a sheet of paper is what lets this happen. The question about ‘pressing into molds’ is contemplating the reverse: that the paper is being compressed.

This of course is wrong. A thin moistened sheet will sometimes blister, or its edges will ripple, because locally the paper has expanded and has no where to go but up or down. (A fine, interesting article on this subject was published last year by Eran Sharon.) But in origami that is never an effect you want, as it is entirely uncontrollable: indeed one uses thicker, more absorbent paper precisely to avoid any such blistering. If you get wrinkles or blisters from treatments that involve liquids (e.g., when you glue sheets together or prepaint using inks or watercolors), you’ll probably leave the sheet overnight between flat boards or under a sheet of glass, to salvage something of your labors. At all costs you want the sheet to be flat.

So if wet-folding does not alter a sheet’s “Gaussian curvature”, what does it do?

Let’s define things. Wet-folding in origami is the process of lightly moistening your model as you fold, with a damp cloth or spray mister; sometimes the moisture is applied only to specific regions.

It serves three main purposes. (1) It changes the way paper responds to indentations, and hence gives folded paper a softer and more rounded look. (2) It allows stiffer papers to be folded without cracking. And (3) it releases and repositions the sizing or glue that some papers are made with, so that when the model dries it sets into the 3D form you left it in with great permanence (I recently had occasion to handle some Yoshizawa works from the 1960s, they are as stable & solid as if made yesterday—and will be, I bet, in 500 years.) In short: wet-folding is a sculptural technique, a temporary softener of paper, and a great stabilization method.

I am most interested in origami’s aesthetic and sculptural properties, though these too of course have a physical substrate; so let’s focus on (1).

Wet-folding allows paper to take dimples and indentations softly & evenly. The look of this contrasts with dry folding, because dry paper prefers to take folds that are straight lines, or alternatively to crumple (= form straight-line segments with messy twists around vertexes, and mostly flat planes.) When paper is wet, it behaves a little more like cloth. Pressures dissipate not in a crumple-pattern but continuously. The result is that visually, you are dealing with surfaces --uninterrupted smooth areas where the form is indicated by roundedness, not by fold lines. (And where there are fold lines, they are read a little differently from their dry-fold counterparts: they are thicker, meatier affairs.)

This has a certain inexact analogue in painting, where you can represent forms either via draftsmanship or by what is called (in a different sense from origami) “modeling”—i.e. gradations of shade or color to indicate curving surfaces. (That the mind has these two ways of processing nature’s forms was a fact known & played with by, for example, Leonardo, who likes his painted smiles to hover between gladness and the ache of knowledge. To accomplish this he’ll sometimes use ‘modeling language’ to indicate innocent joy--you can see this better if you let your eye lose focus slightly--and a contrasting ‘linear’ language to indicate secret, perhaps painful knowledge. The smile seems to flicker in and out of existence as your concentration wavers...)

The comparison to the drawing/painting dichotomy is inexact, however, because of course in drawing, a line can be curved too, and can vary in stress; whereas in paperfolding, an edge-line is going to be straight and have identical weight the vast majority of the time. So really what we are comparing in paper-folds is linearity on the one hand, with a model being either flat or 3D but composed of flat planes--these can suggest ‘bones’ or architectural outlines or intellection and abstraction of form--and on the other hand, the thicker and more graduated curving forms, the haunting ‘emotional’ and expressive look of wet-folded origami.

Monday, May 07, 2007

The Minimal Flower

We haven’t had a ‘natural history’ post on this Blog for a while, despite its name which I’m still committed to. But this investigation of flowers is triggering various new thoughts on flowers themselves, not just the origami of them; and its time to put these down---while they’re fresh and crude, in fact. Before a guarded professionalism, the curse of the times, withers their innocent bloom.

First, though, an old thought. No one seems specially surprised that flowers are delightful, exquisite, turn-ons, ideal objects for gifts, distinct and different and inviting of fine discriminations between them, a joy to multiple sense-organs, and connected more than etymologically with much of what we mean today by being “cultured” or “cultivated.”

The question is, why should any of this be. Flowers are basically an invention of insects, who taught the first angiosperms, 125 million years ago, what forms tickle their fancy. Why should what appeals to creepy-crawlers have anything to do with us? It’s been some time since we parted company. The last common ancestor between invertebrates and vertebrates lived 600 million years ago: a marsh-edge feeder, I understand, who had rudimentary vision at best. That there should be anything in common between us today as regards aesthetic tastes would seem a very considerable feat even for the sometimes astonishing forces of convergent evolution.

I have, needless to say, my own thoughts on what drives these confluences that turn up in nature’s aesthetics—which, presumably, I’ll get around to publishing one of these years, maybe after the war. (Hint: these theories are NOT chemical.) For now, though, it seems to me we ought to just be amazed.

Tinkering, lately, with those origami flowers, especially those irregular Miuras, I’ve noticed this: if you make tiny variations in the pattern of zigzags on two flowers that are otherwise identical (in color, size etc), you can’t include them both in the same ‘bouquet’ and expect them to be read as the same species of flower. The eye immediately picks out minute differences in angles, numbers of folds, and so on. Of course, in nature each individual flower unfurls, blooms, shakes in the wind, withers and goes through countless other changes while still leaving enough constants to allow a quick identification of it. Given a flower’s function—to get you from flower A to flower B of the same species on another plant, while bearing pollen—this is not altogether surprising.

But there’s been much talk in recent decades among psychologists, or nowadays, neurologists, about a ‘special face module’ in the brain that lets us quickly read human & animal faces, both for purposes of identification and to read the emotions expressed. That’s one reason, by the way, why it’s trivially easy to make SOMETHING in origami that will look like a human face (the module has a low activation threshold), but not at all easy to make the specific human face that you set out to, expressing a particular emotion, and have it be realistic rather than a caricature (there is high discrimination sensitivity). Now, I would bet that there is some similar module in our brain—maybe the same one—working for flowers too. And this would be another point of contact between ourselves and the insects. (You neuro grad students out there itching for a cute research project---here it is. Plug in those electrodes, see what lights up.)

[>Added February 2010: For a new scientific appreciation of the opposite idea, that insects (bees) have a 'face-recognition module' just as we do, see here. The researchers have not yet speculated on whether the module for recognizing faces is the same as the one for recognizing flowers.]

A question that’s as much about flowers as about the origami of them is: what are the minimum requirements for a thing to look like a flower?

At first glance it seems that almost anything can serve: a splash of color against the green is almost enough. The other day at the Beersheva Library's gallery I saw some splendid abstract, Pollock-like still-lifes by a Russian painter named “Zukhov”, who does just that: some random drips and daubs and splashes--and you have a vibrant bouquet. And in nature too, there are so fantastically many forms of flowers and whorls, the flora seeming to compete amongst themselves to come up with the latest fashions—that it would appear ludicrous to lay down any general rules for when a thing starts to look floral.

But this is origami, and we can't just leave it at that; we actually have to make something. And anyway for me, given the line I’ve been pursuing lately the question arose in a slightly different form. It bears repeating: What is the simplest origami pop-up shape you can make that can reasonably be called ‘a flower’?

This is, of course, an instance of a question asked when approaching any origami design. What is the simplest representation of an X that you can get away with? Or: what is the threshold where a bent-up sheet of paper with a few flaps, creases and bulges, turns into ‘an X’? Or: What will make fellow-designers green with envy at the thought: now why didn’t I come up with that?

Minimalism, I hasten to add, isn’t the only or even the main objective in design, just one possible goal; and it’s of course true that excesses in minimalism can be infuriating--seem to be insults to the viewer's attention or intelligence. (Most ‘one-crease’ origami strikes me that way.) Nevertheless, the minimalist effort does establish a sort of lower representational boundary that I maintain it is always important to find.

One of the simplest forms I can think of that counts as a pop-up, is the venerable and ubiquitous preliminary fold. Pull at the two flat exposed corners, and the two bent corners pop right out; push at those same points: the others climb right back in.

Unfortunately—but interestingly—this shape is not quite complex enough to be read as a flower. Even if you make it from a nice brightly colored square, say red or yellow, and prop it against some greenery. (Try it and see.) It is however enough for representing a simple roundish leaf, if the paper is green.

Here is small variation that makes the preliminary fold more compact, and so perhaps better for pop-up purposes. (Make all interior angles 60 degrees.) But the result will still be read as no more than a ‘leaf’--if even that. 'Design minimalism' may have been achieved, but 'representational minimalism' has not.

With a just trace of added complexity, however, the “preliminary fold” can be made to be read as a flower. Instead of dividing the surface into four, divide it into nine. It will still close back, more or less reliably. There are three main options for how the thing can close, but it doesn’t matter which one does so long as it closes.

Take off slight triangular amounts too from the north and south corners. The bent-back corners help close & open the model a little better in the middle. But they also let you read the slender mess of lines at the flower’s center-region as some visual noise within the geometric pattern: i.e., as the sex organs.

So it seems that what you need from a 'flower', besides a splash of color, is this: a minimal hint of geometric texture—i.e., a pattern. Division into four does not quite constitute a pattern, apparently; and patterns based on odd-numbers seem a touch more ‘organic’ than even ones. Further, a certain amount of noise, darkness or other difference should exist in the center of the form, to invite visual-tactile exploration: if you’re an insect who’s alighted, that’s where you’re going to be pulled to. Finally, I’ve found that the color of the flower really wants a green underline or undercup as contrast.

But that’s about IT. Further elaboration is of course welcome; but these seem to be the necessary minima.

--Is this an observation about flowers, or only about (origami) representations of them? Given that a flower works by putting on a show for us of insect-minds----is there a whole lot of difference?

Wednesday, April 25, 2007


Not all the flowers I’ve been showing (and others I haven't yet) do I fully understand the mechanisms of. For most I have at least a vague sense of how they work, but some are surprising even to me. That is: while looking in certain obvious directions and playing with various forms I’ve across a few that behave as wanted—they open and close reliably and in interesting ways just by pulling and pushing at two points. That doesn’t mean I necessarily know what’s going on.

Of the three principles I mentioned in an earlier post—preliminary fold, Miura and twist—the Miura has perhaps been studied most by physicists and engineers, its pattern having been invented after all by a physicist who wanted a nice reliable way of unfurling and refurling satellite panels in space. Even with this pattern, it seems to me, there is room for further research, and studying pop-up applications is a great way to do it. I’ve echoed the Miura pattern symmetrically across one axis, to take the shape of a leaf or a flower; it folds up just as nicely as the unreflected pattern. How many more axes can this be done for? More to the point: the Miura pattern can be made VERY irregularly, and it will still fold up—in one unvarying sequence, and ending up flat; but pulled or pushed, it will go through an interesting succession of phases before it reaches the end state. (Unlike the regular pattern, which is a smoother and more simultaneous, hence for me a more boring process.) What guides the expansion or collapsing sequence with these irregular Miuras, and their sudden bursts? How much irregularity will be tolerated before the succession breaks down? What happens with radial forms of Miura? And so on. The beauty of origami is that you can test these questions out almost as soon as you’ve thought of them. And if you’re a tenured university professor someplace, you can even write a paper & get a nice grant for doing just that.

At the right level of abstraction, the Miura map fold serves a paradigm for what one looks for in an origami pop-up. --How does it work? A two dimensional sheet with numerous fold-lines usually has lots of options for folding back up when pressed at two sides or points. Some of these options lead to misfolds, as every tourist knows who has had the frustration of trying to close up a normal paper map. What the Miura map fold does is force the two-dimensional sheet to collapse first in one dimension, then in the other. It reduces a 2D problem to two 1D problems, and solves each in turn. You end up with ONE succession of folds, with a single choice at every one of its junctures. –What other fold sequences are like that?

These problems have a math & physics aspect that is not too closely bound to the specific mechanical properties of paper. Solutions would work just as well for a computer simulation, for hinged plywood sheets and indeed, for satellite panels. But some possibilities for pop-ups probably do rely on paper’s properties to some extent. Everyone who has done any significant amount of origami knows that paper has a memory. For almost any model, it is much easier to fold the shape after it has been unfolded back to the flat, than to fold the thing from scratch. I’m not making just the obvious point that existing creases make the folding easier: Rather, of two fold lines on the flattened sheet (say, both of them mountain folds), one made earlier in the fold sequence and one later, slight pressure on the sheet will tend to make the earlier line fold up sooner than the later one—much of the time though by no means always. The paper often has a partial preference for folding itself back up the right way, so that it takes only a little guidance or coaxing to make sure it doesn’t head into misfolds. --Why is this? And as a practical matter: could one design a model or pattern with an eye to just this effect? So that with the minimum amount of guidance, the model would fold itself back up entirely the right way? And using principles that have nothing to do with Miura folds? --It seems to me this too is a feature that a proper investigation of ‘pop-up’ origami might reveal.

Bestowers of research grants, lurking wherever you might, take note.

Sunday, April 01, 2007

More Blooms

These three are activated: Click to watch them bloom.

No radically new flowers invented since the last post: instead I've been working on everything that surrounds them--the background card action, the necesary leaves, stems, vases etc; while rapidly trying to figure out how to film these things (my double-chin finally having found its purpose and vocation).

Where things are headed: More and more I want the background card to pick up the non-flower elements; and I'd like to purify this so that the card too is origami as far as possible. Recent experiments suggest that very nice pop-ups can be made of just origami corrugation patterns--I mean, dropping the flowers altogether. I'm a little reluctant to go in this direction as there are some VERY talented people out there already doing similar things, who can do a better job of it if they cared to: I mean of course Fernando Sierra, Ray Schamp, Polly Verity, and Christine Edison, to pick a few names at random. One thing I've been exploring that I don't believe has been done yet by the tessellations crew, is mixing elements which are corrugation-based, and therefore expand in all directions, with those which are 'fixed' or 'hard-folded' and don't (or at most flatten boringly when pulled on).

A book is in the offing: The Handbook of Blooming Origami.

Stay tuned--more blooms may be appearing in the coming days. Its spring after all


to whom it applies: Pesach Kasher VeSameah
Happy Holidays, everyone.


All images, videos, and the underlaying design of the blooming origami flowers on this blog are: Copyright 2007, Saadya. All rights reserved

Saturday, March 31, 2007

Sunday, March 18, 2007

Blooming Origami

Just in time for spring.

Click on an image to see what happens.

The idea here is

(1) the opened flower should have much more than twice the surface area of the closed one; it should not just fan out but expand in all directions as it opens.

(2) It must close back reliably the same way.

(3) Should be pretty, and look like a flower.

(4) If possible, it should change dramatically through different stages as it is opened.

(5) The flower must be origami—from a square, no cuts, and glued only to the background card.

The only mechanisms I know of so far (but I’m pretty ignorant) that do any of this reliably are the preliminary fold (opens to 4X; & with a variation, to 9X), the Miura fold (opens to an indefinite multiple of X), and twist folds. All of the flowers shown combine these principles to one degree or another.