Pajaro para Román

In honor of his new book.


-------------------------------


Another version.







[Added December 15:]

And---here's a set of images that no origami designer can fail to be inspired and humbled by:

http://www.nytimes.com/interactive/2009/12/15/science/20091215-birds-audioss/index.html

Animal Signaling, Origami Liveliness

This is mainly a ‘natural history’ posting, not an origami posting, but you origami people should all read it all the same.

First off, have a look at Olivia Judson’s fine article in last week’s New York Times science section. It is about how animals have different calls to warn their group-mates about the approach of different kinds of predators.

* * *

Neat, no?

I touched on this subject once before back when starting out on this Blog. This was when drawing attention to just how weird the Owls look, among all the avian species; in particular noticing that (a) all owls have haunting, rather 'unbirdlike' faces, (b) many owls have specifically mammalian-looking faces, and (c) some owls have even more specifically a face that looks like a cat's (facial feathers that resemble fur, pseudo-ears that resemble cat ears, a hook nose flattened against a flat triangular face, yellow eyes, etc.). By “cat” I mean of course not just the ferocious predator known as the domestic cat—but it too.

Suppose we grant the observation. Why would an owl want to look like a cat? What do the two even have in common? Casting about for an explanation, I speculated that this might be a form of mimicry directed at the prey. If the owl, sitting in the bole of a tree at night, can trick the rodent or small bird into thinking it was a different sort of predator—and cats are the main competitors for the same sorts of prey Owls go after—it will trigger the wrong escape-strategy in the prey animal, and thereby gain an advantage.

Now, this was almost the subject Olivia wrote about. Actually what she discusses is a more general and more fascinating phenomenon: the fact that that some prey animals have distinct calls for warning troupe-mates about the approach of different kinds of predator (e.g., one call for an eagle, another for a leopard). But the direct implication of her account is that there must be a different correct way of reacting to each of the different types of predator. Maybe the optimal escape-strategy is ‘freeze’ if it’s a cat, ‘get to the nearest tree’ if it’s a bird: I don’t know the details (few of which have seem to have been researched, so far as I can make out). But there has to be a difference—or the different calls would not have evolved.

And if that’s the case, it pays an owl to look like a cat.

* * *

What does this have to do with origami? Very possibly nothing. Except that good origami animal design tends to involve a great amount of close observation of actual animals, and a lot of thought about animal categories. This bears repeating. The thought that goes into the design or execution of good origami isn’t just folding-thought, or even just or primarily geometric thought (as might be concluded from some of the ways origami is being pitched to the public nowadays) but science and sensibility much more broadly construed. I think it’s already true of this young art that in the history of sculpture in the world there has never been as wide or as detailed a study of the forms of so many different species, in any medium. This sculptural study is being carried out by some fairly intelligent people who insist on 'getting it right’ and who also care something about the animals themselves, along with their representation in paper.


Also it seems to me: origami still has the advantage of being a borderline art, even as it claws its way toward respectability. For a long time it was practiced and transmitted in the West by magicians, and in the East by members of the ‘floating world’. Something of this marginal existence and tolerance for—even courting of—unrespectability is part of its essence. Yes, we have to be intellectually disciplined, rigorous with the folds, or the thing won’t come out—but we still have a liberty of thought that you rarely find in academia nowadays. (Maybe encouraged by the material's manipulability: you can as easily fold the sheet this way as that, because in the end ‘its only just paper’.) Given that we have no reputations to lose, or maybe have lost them already, we can afford to make risky speculations, backed as said by a great deal of observation and reflective musings as the paper is fiddled with. If you suggested an idea like the one above at a university, the hoots you’d hear would not come from the owls.

* * *

Olivia Judson’s article also contains a striking photograph of some Diana Monkeys, taken by Tim Ockenden for Agence France-Presse.

Now, each time I see one of these pictures, or see some well-made animal paperfolds, I come back to the strange question, why on earth it is that origami is so suited to the making of animals---I mean, where does it get the ‘life-like’ quality it is so famous for, and why is there more of it in folded paper than in works made from stone, wood, plaster, bronze or now plastic.


With these Diana monkeys in the photograph the question is slightly less acute, since there’s a beautiful color change and one that seems as if crying out to be reproduced in duo-colored paper by, say, Quentin Trollip. Birds, for instance, often pose a greater problem for origami than these monkeys, since a common color number in birds is three rather than two, and paper unfortunately has only two sides. (I will discuss the question of why animals have the number of colors they do, hopefully in another post.)

As to the general problem of what is specially ‘lifelike’ about this medium, I confess it’s still a mystery to me, even after years of thinking about it hard. But let me take another crack at it.

* * *

To fix ideas, let’s use a concrete example. Hard as it is sometimes to tell things from photographs—here is an image of Roman Diaz’ Elephant .

Here, the folded form is 3D, and in that respect more lifelike than simpler forms. But still it is exactly missing at least two very prominent aspects of actual, living elephants: the thick, impenetrable mass of that body and its supporting columns; and also—let’s not forget it—that elephant smell, which is the smell of a zoo. And even so, or perhaps for that very reason, there is an incredible amount of ‘liveliness’, ‘presence’, and ‘potential motion’ to this folded form.

One idea that suggests itself to explain this liveliness is that of the ‘ricochet’. 'Life' or 'liveliness' is, in a sense, what you are left with after you subtract all physicality and substance from a corporeal being. But 3D origami from dry paper is also a 'subtraction' from a massy representation of all its mass: it’s another way of ‘bouncing back’ or ‘ricocheting’ from the expectation of substance. And maybe that's why it suggests its counterpart: life or liveliness.

This is a cute, probably too-sophisticated idea, but the first problem with it is that an origami animal is not just the skin or outer surface of an animal, done up in paper. It is not, for instance, a paper version of a cicada's nymphal shell. Part of origami is the folds, not just the material. If you were to somehow render just the outer surface in paper, you would not get the full lively effect that origami animals are able to achieve.

Or so I claim; but whether this claim is true or not it at least it has the virtue of being not theoretical. The closest anyone has come to to making 3D paper outlines of an animal’s surface is the paper-and-wire sculpture of Polly Verity, who is known in the origami world for her leadership of the field of curve-folding but not for animal origami design ‘proper’ so far as I know. Yet have a look at some of these (mythological) animal sculptures she has made.

They are elegant works, maybe the best of their type; they use paper on a wire frame and gain a gentleness from paper’s translucence and fragility; and some of them include origami elements (tessellations) along with the other manipulations of paper that involve cuts. So they draw on some of paper’s qualities and some of origami’s too. I would even say that as finished art products most ‘regular origami’ would have a hard time competing with them. Nevertheless they are not strictly paperfolds and it is my impression that they don’t get all the way to the liveliness that ordinary animal origami can reach, I would say more cheaply.

But look for yourself, and judge for yourself.


What all of this suggests, if true, is that the integrity of the paper, and the visible folds, are essential, necessary elements in generating the liveliness, along with the use of that material, paper.

* * *

I want to risk introducing another ‘natural history’ idea into this mix. The basic idea is that origami is using the language of flowers to represent animals with, and flowers are a little different from animals in their signaling qualities.

From the origami side, the idea is that, in being made of a flat colorful surface which folds and unfolds its way into its final shape--that is, suggests the possibility of its form being made and unmade by folding, growing and changing in the now--- origami is using some of the visual language of flowers. And so if you are making an animal via origami, you are extracting and applying the distinctive attractiveness and fragility and disarming properties that a flower has and giving them to the animal, which has them only in part.

From the natural history side, it is worth asking what differences there are in the kinds of beauty (or attention-striking properties) a flower has, as compared to an animal, and why these differences exist.


Though the notion has only been around since Darwin, and has only been taken seriously in the past 30 years, and still is under-appreciated in my opinion---a good deal of animal form and coloration is driven by sexual selection, and some of it by other types of signal selection too (signaling to parents, signaling to offspring, social-status signaling etc.). But sexual selection itself is not monolithic: it has the two rather different functions of attracting females and threatening away male competitors.

In animals, these two functions are sometimes performed by the very same signals. In other words, although nature has evolved a fairly universal language for signaling threat (especially ‘aposematic coloration’ or warning colors), in animals, some of these very same signals, or modified elements of them, get used also for the opposite purpose of attracting a mate. In animals, then, there is a certain blurring in how the signals evolve as between ‘come-hither’ indicators and ‘stay away’ markings; these tend to take over parts of each other. If an animal has a striking feature, it may or may not be used to fascinate a female with, but chances are that this conspicuous feature is also a warning.

This is not true of flowers. A flower’s signal does not contain any element of threat. It is meant simply to attract visitors and disarm their wariness as it tricks them into serving it and shakes its pollen upon them. If a flower is not ready to attract, it does not broadcast its signal; if it wants one pollinator to come but not another, the most it does is broadcast on a perceptual channel unique to its preferred pollinator (e.g. ultraviolet colors for bees, red for birds), shift its flowering schedule, etc. What it does not do is broadcast signals that are also threats. I can think of virtually no counter-examples to this ( the "Bat Flower" might be one). --A flower's striking qualities are all attractions.

That means that flowers are a purer case than animals for studying the evolution of the language whose meaning is 'come-hither'. So if you want to see what evolution can do when it is driving forms purely to attract, flowers are where you should look.

* * *

What are the consequences of this for origami?

(1) If you think that origami is borrowing flower-language for its representation of animals , then animals are getting an 'added value' by being done up in paperfolds. They are getting the disarming, inviting quality of flowers—which even the actual animals don’t have (or maybe it is masked by what’s threatening in them, and takes some extra empathies from us humans to notice them).

(2) If you use origami not for making animals but for making flowers, you might get a closer representation of your subject than you would, say, from using plastic or fabric. But even if you did, the added value would be less than it is with animals. For now you are competing with flowers on their own turf. I say this of course without my admiration dropping by one iota for those--like Olga de Pedro--whose sense for the colors, folding and arrangements of paper flowers is impeccable.

That's it for tonight.

Saadya

October, 2009
Beersheva, Israel

Possession

Last night I went to the opening of a small exhibit by Ilan Garibi and Herman Mariano, at the Henkin gallery in Holon, Israel.

Garibi: strong folds, clean, tasteful color choices and combinations, voracious explorations of his new love, tessellations, some of which are more muscular than a lot of the delicate-and-fussy things I’ve seen in this line before.

Good to recognize a new force on the scene here in Israel (even if I’ve been slow to do so, hiding out as I have in the desert.) Pleased to meet the person too, for further qualities of character not immediately evident in the folds.

I will let these images speak for themselves; but see also here.

Good also to see the tradition of origami-themed shows being upheld in this space: the last one here at the Henkin was mine (five years ago---way too long for this space), and before me came Tomoko Fuse, and before her Paul Jackson.

There are some real origami powers in this country, but they are scattered. The group Ilan belongs to has a terrific set of people but for various reasons has been able to retain perhaps a third of the known folders of quality in Israel; and the unknowns, whom one catches sight of at various events, probably outnumber the knowns. Maybe Ilan is the man to heal the rifts and unify the ranks. We will see.

The other exhibitor here is Herman Mariano, who I’ve written about before on this Blog. I think, up to about 4 or 5 years ago, I could claim with some confidence that this retired architect was the best folder in the world of origami animals, who is not himself an origami designer. And if I can’t say that now it is through no fault of his own—he continues to advance, well into his 80s—but rather because origami has exploded in so many directions now and there are so many new talents lurking that any such a statement would be incredibly hasty.

Actually, good enough as this show is for the masses who have no other option, the real treat is a visit to Mariano’s home, an origami household the way one imagines but rarely encounters it, the animals perched on the bookshelves in front of the texts. And the books themselves—besides the very large origami library there are all the wildlife volumes and videos that he studies each time he prepares to fold an animal model. Tucked away in odd nooks and stashes is his paper collection, the finest I’ve seen, brought in from all over the world or purchased on whim; papers for which Mariano has developed his own treatments to color and stiffen as needed. Those who come to the exhibit can see perhaps some of the products of all this industry; but for me the special delight is that apartment itself, with the ‘morning energy’ it exudes. Cleanness, color, order, youth, readiness for work, ranging intellectual interests, eagerness for study, experiment and exploration: music. The whole shining glory of origami in a few dozen square meters.

* * *

I have to confess that my first reaction--by no means my last--to this show, this quite tastefully arranged exhibit, was to frown.

For you see, some of those Mariano-folded animals--perhaps a half-dozen of them--had been in my Tikotin Museum exhibit a few years ago. And here they were again---“my” pieces, now placed in new positions, set among different companions. Somehow I had come to feel proprietary about them, I mean, as if I had designed or made them myself, to the point where I was vaguely annoyed that they had been moved about and joined with other fellows at all, let alone without asking me.

This is of course nonsense, but I am reporting the feelings as they occurred. And will take the time now to worry about them a little.

It sometimes happens with a complete stranger, a beautiful woman—a certain kind of beauty—that you feel a mixture of ownership, physical kinship with her, I mean quite as if she was a daughter or sister or something. You see a part of yourself in her; and then you feel like you have rights. Of course she is herself entirely hers, but now owns a part of you, is the truth of it. But you can’t shake off the impression, the mutual belonging, the sense of possession. Some of that can happen with origami too.

I knew a woman once who had played with folding paper as a young girl, quite on her own, not knowing that there even was such field as ‘origami’. Later she visited Japan; and when she came back she began publishing a series of origami diagram booklets on the cover of which her name appears in big letters, while inside the preface extols the unique educational properties of her diagramming technique. Meanwhile the names of the designers of the models (Yoshizawa, Francis Ow, many others) had all mysteriously disappeared. For, you see, those designers had come up with the same things she had already thought of as a girl (more or less); so they were hers. Today, if you press her on this admittedly delicate point, she is liable to add: she’d thought all these models were “traditional” (rather a stretcher, as she must have learned them either from books with the author’s names clearly spelled on them, or from teachers who would have named them for her.) But never mind. I see this as an extension, maybe a little more extreme, of the same possessiveness that all good origami can arouse. One falls in love with a model, learns it, folds it, and then it becomes part of oneself. All sorts of feelings from childhood attach and surround it. It is easy to start imagining one has rights.

Proprietary or territorial feelings can be awakened even with something so transitory as an exhibition space, when once you have put up a show in it. Mind you--this is not a space you ever owned or even rented: all you did was inhabit it for a few weeks or months, invest all your heart and soul in it; and now, it seems to you, by golly, it is yours in some way! What are these others doing in it! Yes, it is a pretty exhibition, you fume. But surely your successors must at least owe you something merely from the fact of you having been there before them, maybe cleared the way?

This is nonsense, and one had better get over such resentments quickly if one is to enjoy the show, or anything else.

* * *

Ah, pride, possession, ego, rights.

A few years ago I put up that exhibit at the Tikotin Museum of Japanese Art. I worked hard on it, with the very limited resources and limited international reputation I had at the time, but with some solid friendships. It ended up being a great success--strong reviews, enthusiastic comments from the public, record crowds for that museum and so forth. It was a significant moment for origami on the Israeli landscape; and it mattered to me that this be done in the Tikotin museum, which is the institution with probably the oldest connection to origami in this country (first via Felix Tikotin’s direct association with / assistance to Yoshizawa in the 1950s, and later via Eli Lancman, the museum’s director for many years.)

But what I most wanted, and I think achieved from that show, was to set a high bar for the display of artistic origami---as high as the display of any prestigious work or historical artifact in any major museum of art today. I had strong material to begin with, gathered from all over the world, and what I most wanted for it was respect.

Now as it happens, a "successor exhibit" to that one, in scale of ambition if not in size (in size it is double), is taking place right now in a museum in the city of Zaragoza, Spain. "Origami, El Arte del Papel Plegado", is at the History Center of Zaragoza; its curators are Felipe Moreno and Jorge Pardo (I understand it is a production of the Zaragoza municipality, the History Center,the Aragon origami group and the AEP.) I haven’t seen it or very many images from it but by all accounts it is a smashing success. Over 20,000 visitors have come in just its first month; it is the best-attended show in Zaragoza at this moment, has broken all records for this museum, lines forming around the block on weekends (where the group’s folders are giving impromptu lessons), students being bussed in from the schools and a waiting list of thousands of pupils.

I am pleased without qualification in their success. And also proud. Not all of us can design models that change the field or steer it in a particular direction (or, not all the time…). So if one wants one's field to flourish and grow, and also to have an influence, then one would like ones words to allure or sting; one's images to excite and linger; one's half-baked idea to induce its completion; one's moment of courage, to generate further courage. If that Tikotin show played a role in piquing the regional pride of the Aragonians into concerted action or or set an example of any kind, I could not hope for more. And if their show now raises the bar for those who come after them, they will have done well.

But I can easily see, with a slight twist of the screw, how such pride and satisfaction could turn into pride-of-possession of a very different kind. If I was built just a bit differently I might now be grumbling at being outclassed. I would be saying to myself: “Why, they never would have done this if it wasn’t for me…” “If I hadn’t recommended him, he would never have…” “If they hadn’t seen the photographs…” “If he had never met …”

Nonsense. The Zaragoza group is the oldest origami group in the world, dating back to the 1940s: it existed before every other formal or informal organization of paperfolders. Felipe Moreno has been its heart and soul for a very long time now--you can see him in those old, black-and-white photographs. The Aragon group and the larger AEP organization have demonstrated great efficiency in their conventions and exhibitions, seem able to work in marvelous unison—have somehow managed to overcome the tensions which have crippled the public expression of origami in several countries that I know of.

As a general rule, it is unwise to take credit for another person’s existence, or art, or success; there are few things as guaranteed to produce ill-will. With origami it may be worse: people who do it seriously as adults are liable to have started in childhood, years before you met them; when you take credit for what they now do you can expect them to feel you are laying claim to some of their most deeply anchored experiences. And of course, if you do not just claim credit but try to cash in on perceived rights to gain special privileges of one sort of another, you have crossed from private delusion into public venality.

The other side of this coin from the assumption of rights and privileges are assumptions of gratitude. In this field one had better feel grateful for one’s precedents, because there are a lot of them. Every one of us stands on the shoulders of giants, and has cause to be thankful for great numbers of people in our still-small circle: for their models, publications, teachings, techniques, social organizations, generosity--for labors which in the vast majority of cases have been ones of love, done entirely without remuneration. Not one of us stands alone, is self-made. Our community is a web, and it must not be jumped on too heavily, even as the bad apples are shaken out.

A slight propensity to take excessive credit for oneself, when married to a full-blown personality disorder, can have explosive results. For if there is no restraint on ego and possession, it won’t be just other people’s models that are taken without mention, and not just exhibition spaces that come to be “owned”--permanently--but entire geographic areas that are laid claim to. The sharing and collaboration that is a basic feature of origami in some parts of the world, will be turned into its opposite. Origami events, private gatherings, commercial efforts, educational undertakings, maybe even the act of folding itself alone in a corner, will in that person's mind have become a private possession, subject to his or her exclusionary rights. “Any origami that takes place in the region of Nagtamar,” the Evil Queen was heard to say, “either goes through me or doesn’t happen at all.”

In speaking of 'rights' and 'possession' in this blog post I have not touched on the issue of copyrights, a subject over which much ink has been spilled. But it is clear that the same people who have a distorted sense of their own entitlements, are the ones that will play fast and loose with copyrights too.

It may be that the philosophers of old were right, and there are no pure vices: every vice is an exaggeration of what in healthy proportions would be a virtue. For ego, possessiveness, territorialism, are essential in this field too, in their right measures. If you are a designer you damn well better feel proprietary about the form of origami you have staked a claim to: whether it’s modulars, tessellations, birds, insects, pleat-folding or whatnot; and if some pimply-faced newcomer dares to make an entry in your field that meets or surpasses your own, you are no designer if you don’t itch and sweat a little. You had better get cracking, learn what he knows, and do him one better. That is territorialism, competition in its healthy sense; not the exclusionism and expropriation that is antithetical to the spirit of origami.

Ilan and Herman---I enjoyed the show.

Ilan Garibi’s and Herman Mariano’s show runs at the Henkin Gallery in Holon, Israel, through November 8, 2009.

“Origami, el Arte de Papel Plegado”, runs at the Centro de Historia de Zaragoza, Spain, through 21 November, 2009.

Beards

Nine-faced Jar

It was time to make another of these, so I did.

Folded from an uncut rectangle of foil-backed paper, two edges glued to form a cylinder.

9, because I wanted the viewer to see about 3 faces at once. (And because 8 is a boring number.)


Known inputs. A pot with faces I glimpsed at the Art Institute of Chicago in the 1990s, probably from bronze or ceramics; those little figures adorning portals to cathedrals, which from a distance look like pencil-marks or charcoal scraped on paper; David Huffman’s beautiful Tower Form. Thoughts about how the figures in a bas-relief are in process of freeing themselves from full immersion in their background (as in painting) to full independence in our world (as in sculpture)---and so thrive in this half-subservient state. Studies of face-making folds over the years, seeking always the minimum necessary lines . And technical investigations into curved folding.


About just the latter, a few words.

Apart from the pretty shape, I am showing off two kinds of curvature.

1. Curved hinges. Note the lines that descend from the top and taper inwards. Each line curves, but it bends to neither the left or the right: it is straight in the X and Y dimensions, curving only in the Z. And even so the planes to either side hinge along it. (Which fact is highlighted by contrast with the straight folds emanating from the bottom, which seem to behave normally.) This is not so common even in the world of curved-folding.

2. Bulges that emerge suddenly from flat areas, sometimes without the benefit of hidden folds, pleats etc.


A reaction I'm always happy to get to my curving origami is, ‘I don’t see how this is even possible’.

To which a response is: Sometimes, when you find that the one thing you have to do is impossible, it might still be that you can do two things, both of which are impossible, except together.


Saadya

posted also on Flickr

Ripple-Pop

Going through my files, I found this short video from a few months ago, that I thought you might enjoy.






By the way: In the month of August I will be traveling--by train through Central Europe, with ‘origami stops’ in Prague, Budapest and Zagreb; then on by plane to Toronto and by car to Algonquin Park (and by canoe to the interior). Then back to Israel.

If you or your group would like to host me or meet in the above cities or points in between, send me an email.

Saadya

Sphere from a Circle

Here is a new method for folding an uncut circle into a 'sphere'.

1. Fold concentric circles
2. Divide disk into equal-sized pie-slices (any even number will do)
3. Draw zigzags along the radii
4. Reverse all folds in alternating pie-slices
(or in a less elegant version, just crimp the radii)
5. Fold up
6. Secure with pins

In this technique the sphere is not hollow. The main difference from the more usual way of making spheroid shapes in origami is that instead of folding up 'walls', one folds polar cross-sections of the sphere. In fact this sphere has the odd mathematical property, that its center is the center of the circle, its "surface" the edge of the circle, and all points in between on the sphere are in the same pair-wise order (in distance from the radius) as in the circle.




Greater accuracy and surface coverage can be obtained with some effort by using many 'wedges' (=pie slices in the original circle; looked at side-on they are 'arms' or 'meridians'). But since the height of the sphere shrinks in direct proportional to the number of wedge-pairs, you'll get a perfectly delineated ball only at infinity, and then it will also be solid--and the size of a point.



____________
Added June 2010

Here are a few further points of interest about this form.

• This Sphere is related to the Concentric Winder. Imagine each of the layers of the Winder 'peeled': reverse-folded-along the same diameter line, at various angles, so that the Winder is 'rotated in space'. You will have something like this Sphere. (Some such idea was part of the conceptualization of this model.)
• Like the Winder, the Sphere also offers a negative illustration of the Albers Effect: Because of all the movement back and forth, the surface of each wedge can remain flat-on-average, without being forced to twist from its plane as it does with Albers disks or Yenn annuli.
• Less obviously, this Sphere is even more directly related to the folded Albers disk: for the latter too has circle-lines marking off approximate outlines of spheres. (Because of all the Albers twisting this is harder to see.)
• Perhaps the most surprising aspect, besides the directness with which the wedges rotate and condense into meridians, is that the initial paper circle has one curvature, the smaller sphere another, and yet the circle just magically adjusts its curve to oblige the needs of the sphere. Moreover it does so no matter how many wedges are put in, that is, regardless of the relative size of the sphere! Somehow everything always works out.
• I put my name on this Sphere, for its simplicity; that doesn't mean there are not more complicated things to be made by following its principles. This is new ground, there is considerable scope for variation--so go discover something for yourself!
  
  
  Finally I have to admit---I got lucky here (though it wasn't just luck, as I was actively looking for a Sphere in the month before I found it). --If anyone should have discovered this principle before, it should have been Josef Albers 80 years ago. He after all was asking the right kind of questions, viz., what can you do to a sheet or a pattern that will cause the surface to change its expected behavior. This led to his discoveries of both the Concentric Circles fold and of the Hypar. In retrospect I see now that this Sphere is a cross of those two Albers shapes, though that's not at all how I came to it. But Josef Albers did not take this step: his loss, and my gain.

Cheers!

Saadya


Related Posts:
Concentric Circles (March 2008)
Huffmanesque (January, 2009)
Organic-Circle Fold (March, 2009)

Organic Circle-fold

Faced with a Circle, one draws a blank. Where to start? The shape is too symmetric: a blind eye. How, where, will you find different parts in this Unity? And supposing you do: what creases can you put in, that will possibly preserve anything of the circle's original circularity?


Some of these problems, as it happens, are faced by living forms as well. By the fertilized ovum, a single pregnant cell, or by its descendant the blastula, the nearly homogenous sphere of 1000 or so identical cells. These too must divide or fold, to create form. The sphere in nature solves its problem, breaks its symmetry—by gravity perhaps, telling it which side is up and which down, or by some accidental imperfection on its perimeter. In the blastula a fold line arises (the ridge of it assuming special significance later on) and the whole magic of gastrulation begins: nature's origami on steroids. And then differentiation, growth of the different regions can proceed, each part developing according to its own strict rules.

I tried something similar with this circle, making the most obvious division and then applying the most obvious distinct pattern-folds to each part.

The resultant form is ‘organic’ --- reminiscent of how organs emerge in plants and animals, with intimations of branching and budding and leafing and embryo-curling. ‘Organic’ too in the sense more usual in art, of a thing that is like a living form but is not specifically representational.

Curve-folds, and corrugations generally, have this quality that is present in some but not all origami: in principle you can see all the folds at once. There is nothing tucked away, nothing up your sleeves--there are no sleeves. The magic is all out in the open. So the continuity that is key to origami's aesthetic, the sense that the thing is an integral whole despite all its details, is even more apparent than usual. That too can help make an origami shape seem more "organic".


So, this is one thing that can be done with a Circle. What else can?



Related Posts:
Concentric Circles (March 2008)
Huffmanesque (January, 2009)
Sphere-from-a-Circle  (May, 2009)

.

Curve-fold Fountains

(or: "Feather Caps")










Made from an uncut... semicircle.

As usual I am exploring the interactions (geometric, aesthetic) between curved folds and straight ones.



Saadya


-------------------
Added March 7:



"Angels Instead"

Made from a circle with a radius cut.

toward a Buddha paperfold

Borrows an idea from Giang Dinh.
Made, as it happens, from a square.

S.


--------

Added Feb 28:
And since the technique exists anyway, one may as well apply it.

Fanwheel Flasher

This is in the ‘so simple it seems to have been overlooked’ category. Or maybe it was just too obvious to mention. In any case I haven’t seen it before.






It is just an ordinary fan from a rectangle, with one edge glued to the other to make a full circle. Only, instead of the corrugations meeting the long edge at 90 degrees, they meet it at slightly less. That small change is enough to allow the whole thing to collapse, as a regular circular fan cannot.

This is another instance of the guideline--I hesitate to call it a "law"--that in collapsible origami, skewed angles work better than perpendiculars. Perpendicularity is all about equilibrium, among multiple options and stresses; skewedness is all about disequilibrium--and decisiveness.

If you make this, don’t forget that for a fan to form a circle, the long edge of the rectangle must be at least 2pi times the short one. A ratio of 6.5 to 1 is a reasonable approximation.

How it came about: I’d been studying fan disk shapes made with curves instead of straight lines, some of which are like those which Nishimura and Christine Edison have also been making. These disks collapse to some extent---that is one of the first things one notices about them. Always on the lookout for “special properties of curved folds”, for a while I thought the collapsibility was a function of the curviness. Alas: closer inspection reveals that it is because curves are, by definition, not everywhere perpendicular to the long edges. Simple curves either hit the bottom edge at an angle, the top edge at an angle, or both. It is that angle, and not the curviness as such, that is doing the work of allowing the collapse. And an angled straight fold does a better & purer job of it than a curved one.

It is hard for me to believe that the familiar paper fan, one of the oldest of forms in origami, can give up ANY new tricks at this point. But you never know. If anyone has seen this before, please drop me a note. --Until I hear otherwise I’ll claim this one as my own.

invented December 3, 2008

Saadya



P.S. Ray Schamp just pointed me to the beautiful and comprehensive images in Nojima Taketoshi 's M.A. thesis on collapsible forms. This shape does not appear, but others using a very similar principle (from a flat disk instead of a rectangle) do.

Huffmanesque

This is, I believe, the first successful reconstruction (with a minor extension) of the beautiful Concentric Circles form by the late David Huffman.

I wrote about this form once before, and was a bit brash and over-confident about it. It is NOT a simple cone with concentric folds about its center, as I then thought, but is slightly more sophisticated.

Mea culpa. In my own behalf I can say

1. It’s very hard to tell things from a photograph, especially a face-on one that flattens the object

2. None of the other people who have written about this, and who ought to know, got it exactly right either

3. If it weren’t for my mistake, I would never have come up with that neat wind up toy. Which it seems now I can even take credit for.




Invented March, 2008. I've written about this form elsewhere.



Here is the Huffman idea again. A pattern of serene geometry, an otherworldly form.

Saadya






added July 1, 2009: I just saw essentially the same explorations of cone-folding in Ron Resch's gallery, dated to 1969-1970. He and Huffman knew each other; but I have no information on who looked at these ideas first. Still, Resch's published explorations of cone-folding (no longer available on the internet) are much wider.