Miura

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.

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

Meanwhile:

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


Saadya


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

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.

Origami and Pop-Ups

Having had zero experience of pop-ups till last week, common prudence would suggest not wagging my tongue on this subject at all. But Prudence, Dear, you’ve never really stopped me before, and my tongue hasn’t wagged for a good few months now. It seems to me that thinking about pop-ups sheds a little light on the nature of origami too; so here goes.


Some of the magic of both of these ways of manipulating paper is the same: you start with a flat surface, perform a simple action or series of actions and Presto! have a three-dimensional form, or a shape otherwise of visual interest.

Moreover—manifestly in pop-ups, but implicitly in origami, the process is reversible. You close the book and the form tucks itself away; or you unfold your glorious insect (heavens no!) and get back the original square. —It suddenly strikes me that this unfoldability may be at the core of the origami rules, don’t cut, don’t glue; and possibly at the heart of the feeling people sometimes have (only reinforced by the choice of a flimsy material like paper) that the formed origami object isn’t quite an object, but an ‘object-in-becoming’, on the verge of existence. For the hand in origami can always be withdrawn; no final decisions have been made. What’s done can be undone. No cuts, no glue: that means also, no commitment: nothing’s been sliced away & thrown to the trash, or joined in a union which no man may pull asunder. --No doubt too, that accounts for the appeal origami has for some of us terminal procrastinators. Grow up, they keep telling us.

Pop-ups, of course, do use cuts and do use glue; liberal amounts of both. I was struck by this when I tried to make a pop-up that combined an origami element with other effects: how different the feeling is, when you take up the scissors. Integrity is lost; and one feels quite the sinner, violating that membrane.

The brain too is differently tasked. Pop-ups when done by the masters can show great cleverness or intelligence, but the genius, one feels, is distributed across the page, and is combinatoric: parts keyed & notched together to form some rich, total, tandem effect, from an economy of movement on the part of the viewer/reader. In origami, by contrast, the intelligence is sequential, and is distributed more in time than in space: your result has a long history of folds behind it, not the simultaneity which is the hallmark of the pop-up. One long event in time, giving rise to a single object in space; as opposed to one short event in time, and a multiplicity of interacting objects in space.

Also, though it seems stupidly obvious now, I just hadn’t thought of it before: Most origami models are created through compaction of the initial material. Things end up smaller than the square or rectangle you started out with. There may or may not be a stage of enlargement, when you open the folded-up thing part-ways, pull at the base of the boat to create a glorious hull, open out some flaps to reveal a fine and sturdy box. If so, and only for that stage, origami exists in the condition of the pop-up, with its expanding surprise. But the pop-up lives in that state always, which is the opposite of origami: a form emerges from the stretching of the bundled-up thing, from the unfolding of it. [A pop up invariably starts from the flattened state, but what each of its parts is trying to do when it opens is achieve an even more flattened state (a thinner one), only it runs into obstacles with other parts each trying to do the same—and the result is a 3-D form.]

It’s been proposed that much origami, which has a final stage in which it moves from the two-dimensional to the three-dimensional, can work as a pop-up if the sides are suitably glued to an openable surface. That is no doubt true, but it seems to me you won’t often get the best of both worlds by this marriage. From the origami side it is a little like those compendiums of “climax” themes in classical music: you are given the memorable high points, but without any of the build-up that grants them richness or depth. The creation history, the fold-sequence, isn't what opens to your view except for its ultimate stages. And from the pop-up side, the same 3D form more or less can be made with a lot less bother if you allow yourself a few cuts, as pop-ups typically do; so you might well wonder, why the person has gone to all that trouble. The integrity of origami is a little wasted here.

Closer to my heart is origami designed in advance to function as a pop-up, or to pass through different interesting stages via simple, global moves--pulls, pushes, twists, flexes of a whole surface into a cylinder. The tessellations folks are doing a lot of things of this vein nowadays, although (strangely, to me) the potential for pop-up applications is not being sufficiently explored. Thank goodness, then, for Jeremy Shafer, who hasbeen mining this seam-line now for some time.

Meanwhile, still far behind, here is my first trembling contribution. The flower is straight & simple origami, from a square; the leaf action, in many ways more interesting, is not.


[Video removed; see this post for more advanced developments of this idea. --S.]


Hope you enjoy.


Saadya

For VeganBird

Not Another Swan

“Not another swan!”, groused John Smith, some 30 years after founding the British Origami Society. “[A]fter all, how many new swans do we really need?…Are there yet more fine horses still waiting to be brought into being?”

Did someone say, “Horse”? Hmm…. No. Today we are making a Swan. Sorry, John.

This swan does not inflate, I regret to report. It does not shake its wings when you pull its tail. But it will FLOAT—for long enough, anyway, till you fold another one. And you can teach it to a child.

Instructions (quick version): Make a stretched bird base, double-rabbit-ear the neck, sink a tail, make a head, upend bottom & tail. Q.E.D.


Saadya

Old and New

Horse

I won’t say this is my favorite model. They are all my favorites while I am working on them. But this Horse--I have been with her the longest, starting I think in 1993. Also I have a set of ideals, almost an ideology, for animal origami design, and this is the model that comes closest to embodying it.


1. It is from a square

2. It uses clean angle divisions (15, 22.5) for all major folds (and most minor ones)

3. The preferred angle basis is 15 degrees (which I happen to like)

4. It uses strict referencing till very late in the sequence

5. The referencing is not artificial, but natural (= few/no extra steps just to make references)

6. The number of folds, given what you get at the end, is small (about 40 for the basic, standing version)

7. For horses in its class, paper usage is highly efficient

8. A quite reasonable model is produced with no post-folding, but material enough is there so that an accomplished folder can sculpt it to his heart’s content

9. Different poses or expressions are possible, because many long limbs are independently repositionable without affecting the others (head, neck, mane, tail, legs to a small extent)

10. It is from a Base or ‘embryo’ that can be readily modified to yield other animals

11. No body lines appear on the model that aren’t there in reality, and all those on the real animal are on the model

12. It is closed-back

13. Long limbs are visually continued by body lines

14. It is a beautiful animal.



Shortcomings too may be listed:

1. It is mainly a ‘flat’ model, though it becomes three-dimensional fairly naturally owing to paper thicknesses. (Unlike, e.g., the Pigeons from earlier this month, which are 3D directly by the folds.)

2. Legs should be longer still, to allow proper hooves and more motion poses.

3. While it is ‘closed-backed’, it is ‘open-headed’

4. If done with duo-toned paper, the head comes out a different color, as do the inner sides of the legs. This may or may not be desirable.


As if to balance out these deficiencies: unexpectedly, a version can readily be made that is also an Action Model.


DESIGN HISTORY. Of the three poses shown, the Galloping variation is most recent and has been through only 2 revision cycles (a few evenings’ work) so can’t be called perfect even if it’s good enough to show . The Grazing pose is much older & has been through 3 or 4 revision cycles, the first of them very long ago; I’m not fully satisfied with it either. But the Standing pose, the oldest, has been through at least 7 cycles, beginning I believe in 1993, then set aside till 2004 when I came back to origami. (During which time standards had toughened--for instance ‘open-backed’ animals like this horse used to be suddenly had become 'inferior'). At this point I’m not sure I can improve on this model any further, but you never know.


TRIPARTATE DIVISIONS. The length of the side of the square is divided into three, and so are the main 90-degree angles. The first—the length-division—is pretty much arbitrary; you can vary it and still get a decent animal only it will have a somewhat longer or shorter body which may not be suitable for a horse. (In fact a more perfect Horse can be made with a slightly different division, but I can’t be bothered to establish a reference of "side x 0.31".) The division of the angle into three is more fundamental; for clean folding purposes your options are either 15 or 22.5 degrees, and I happen to like multiples of 15. --Among other reasons because it was less common in 1993 when I started, though it is famously used in David Brill’s fine Horse from an equilateral triangle.


NATURAL FOLDS. A fold sequence can use strict referencing, or it can use ‘judgment calls’ or bizarre fractions for references. The designer most famous for strict referencing is the wonderful Komatsu, and he is liable to devote a fifth or more of the steps in a sequence to establishing marks precisely on the square. (He too has a Horse, of course, and a noble beast it is.) This calls attention to the act of referencing, which is in part why Komatsu has the reputation he has; but it seems to me that a higher & tougher design ideal is to establish references without special moves dedicated to them, that is, to make active, form-creating moves and base each next move on references naturally left by previous ones. Referencing is then no less strict for all that it happens silently.


EMBRYO. I worked hardest here to develop a supple animal base, or what might be called an ‘embryo’, which can be turned into a Horse or into any number of different animals. (It really is like embryology: remember Von Baer’s Law, that organisms are more like each other the younger the stage you look at them, both within and across species.) I prefer to get to an embryo stage much sooner than some other designers do, because this speed is what gives you the flexibility to change poses (or species) if need be.


SCULPTING. I'm a reasonably good sculptor and will often tinker for hours with a ‘finished’ model to get it into the right pose or expression. As a model designer this theoretically puts me in conflict with those folders who want a model at the end of a fold-sequence to come out as close to finished as possible, with little or no post-folding. Actually the conflict is less than it might seem--and enters at a different location than may be thought. Like everyone else, I want a model to be as good as it possibly can be straight off the assembly line. But I also try to design in as much flexibility as possible, so that if tinkerers like me DO want to change things at the end, they will not be locked in by the structure of the model. Designing for maximum uniformity of result is a very interesting concept, but there is also such a thing as designing for maximum variability, and it is not necessarily less challenging.


CREASE PATTERN. Someone who never folds from crease patterns really has no business unleashing on the world a CP of any model of more than minimal complexity. Understanding and skill is needed, to know what to include & exclude. Nevertheless—I promised, so here it is. --A holiday gift: to you who like such things.

Added Dec. 2010: Diagrams for the standing & grazing poses now available in my book, "Sculptural Origami".

Sparrow

I gave in a little too easily a few posts ago to the claim that a bird base doesn’t conveniently allow a two-winged, split back without pre-placement of grafts, etc. Actually here, the desires of the origami designer to show what can be done with points come into conflict with nature’s aesthetics, since most of the time birds are standing around, their wings and tail really are conjoined in one streamlined, seamless unit. But supposing you do insist on showing wing-tips as points—it is not necessary to have them be fully independent. It’s enough to indicate the separation. And if so, a bird base is perfectly adequate to the task.

In fact now that I’ve been around the world, so to speak, with fancy bases and fancy variations to them, I keep coming back to simpler things. The traditional bases turn out to do the job better than the fancy ones! Here is that damn plain-vanilla Bird Base again. And this time I think I can illustrate the idea of continuous complexity directly with this model:

Basically, the moves are:

1. Bird base

2. Color reverse one face of the base

3. Rabbit-ear the other (colored) side around the paper’s squared-off center, while sticking a finger to open the pocket underneath

4. Color-reverse the head too--by loosening the paper almost all the way, making a shallow rabbit-ear, then closing the whole assembly again.


In diagrams here is where you would be in about 10 steps:


One could, in fact, stop hereabouts, or slightly afterward, and have a perfectly reasonable ‘childish’ model. Or perhaps one can think of this as an embryonic stage.

But even if you don’t stop, you should at least pause here, and let the purity and cleanliness of these surfaces and lines sink into your soul. The expanse of unmarked paper, held flat or curving, that shows paper for what it is; and the few long folds, where origami can be seen in its fundamentals. Whatever you do from this point on is going damage the purity of the form. --That may very well be necessary, but you’ll want to minimize the damage, and weigh the benefits of every choice against its cost. Anyone incapable of feeling pain at what about to be lost here will never be more than a technical folder.

To complexify, you might decide to point-split feet, split open a beak, cut the tail into virtual wings plus a tail, ornament the tail further, put feathers on the wings or whatnot. What should guide these choices? There’s a tendency, in today’s testosterone-driven origami, to do what’s technically more difficult, or at least more elaborate, so that you get these scales of complexity: if there are claws, then there must also to be an open beak, wings detached from the joint, etc. etc.

I humbly suggest that restraining one’s gonads here is the wiser course. In design it is generally asked what is the most you can make out of the material you have at hand. That makes perfect sense. But it can also be reasonable to ask, what is the least you can make of it, and still have something worthwhile. For the ratio of means to ends is what finally gets considered, not the absolute values of each. That is the rule for art in general; and for origami, which is all about the Something-from-Nothing, it is true all the more.


* * *

The Sparrow up top is my first experience folding at home with Origamido paper. Boy is it a pleasure! I wish I could afford it! It's what we'll all be folding with in the Origami Afterlife.

Let me wish Michael LaFosse and Richard Alexander a smooth transition to their new quarters in Honolulu. I was born in Boston, even if I don’t live there now, and as a native let me say: this departure is a real loss for the city and for the entire U.S. East Coast. Bon Voyage regardless.


Happy holidays everyone.





[Added 10.29.07]

Pigeon Frenzy

I’m not going to show you two week’s worth of experiments on the Fat Pigeon. My table is littered with bird carcasses, and my brains are in worse state because once I start I don’t stop and now two weeks are gone from my life. The problem, besides the wounded pride hinted at in the last entry, is that I foolishly listened to R. J. Lang two years ago in Barcelona, when he said ‘birds really ought to have their feet point-split’. I disagreed, but out of politeness conceded that “this was at least true for pigeons.” And here was my old Fat Pigeon, standing around pigeon-legged instead of pigeon-toed.

Unfortunately the most obvious way of solving this puts a nasty pleat at the edge of the paper; legs and claws can then be made as long as you like. Now, while I dislike box-pleating I am not opposed to it in principle, if the pleats are put to some artistic effect when the time comes. But here the pleated bulk ends up in the worst place, locked uselessly within wings and tail; and to tie up 20 or 30% of the square just so you can later pry apart some toenails—no, that I will not do. So far as I’m concerned you may as well start with a rectangle or cut the paper.



I have since come up with some more reasonable solutions, supposing feet must indeed be split. But let us first look a little more closely at this assumption, and what is behind it.

Birds have feet, no? So splitting toes is a way of making improved, more representationally-accurate origami—isn’t it?

Not necessarily. Google any picture of a robin or any other small bird. Half the time, do you even see the feet? Feet seem to be something of an embarrassment for bird aesthetics. That is: even male birds, which use flashy colors for their bodies and even sharper detailing on their heads—along with eye-catching profiles that may be egg-like or sinuous—even such birds, who are hardly ashamed of calling attention to themselves, use the universal language of crypsis when it comes to their feet. Feet and even legs on small birds are often thin, reedlike and brown, blending right in to the ground or twig they are perched upon. Sometimes they are knobby and ugly, in contrast to the gorgeousness up above, and in that way too slide attention off themselves.

In other words, a representation of feet may be accurate anatomically without being accurate visually. Drawing attention to them, to show that you are a moderately competent designer who knows how to split a point, is doing something that may be in conflict with what the bird is trying to do, and also with how a bird’s image lingers in the mind.

What, then, is driving the point-splitting of bird-feet in origami, if it isn't aesthetics? It seems to me there are two factors. First is that the older style, from early Yoshizawa, where feet were made by a simple (or a double) reverse fold, really is unsatisfactory in many cases. The bird ends up looking like it is wearing boots. Point-splitting here is a legitimate response to a problem, and is indeed an improvement if (a) you want a stable standing animal and (b) the bird’s feet are going to be looked at anyway. Of course you can also bite the bullet and leave the legs as one long point, or eliminate them altogether as LaFosse had the courage to do.

But a second factor is the current fashion of super-complex, hyper-technical origami, which regards it as an embarrassment if any long points are left anywhere unsplit. A pleasant illustration of this is provided in the Swan by Noboro Myagima, that appears in the AEP Convention Book 2005 (another ‘Barcelona bird’…). The folding sequence is 149 steps long. But at the end of these 149 steps, you do not end up with a Swan which is noticeably better than the ones you learned as a child, that took 10 or 15 steps. Myagima’s model does, however, have one advantage over those older, more modest ones: its feet are point-split. We may note that it holds this advantage over real-life swans too, which, alas, are stuck with merely webbed feet .


Getting back to the carnage from the last two weeks:

I took the Fat Pigeon [CP], a form almost 20 years old--a completely natural, lyrical, geometric sequence from a Stretched Blintzed Bird-Base--and made endless modifications to it, sacrificing purity of sequence for end-results (for we are no longer virgins). To list only the changes I am keeping: Off-centering the Bird-base, allows the tail to be made longer than the wings without additional folds. Off-centering the Blintz buys you all sorts of things. If you want to, you can have a model that’s fully rounded (I mean 360 x 360 degrees). I chose instead to use the extra material from the overlapping ‘blintz’ for various color-changes and also to design what is, at last, a reasonable lock, so the front stays in one piece (without wet-folding etc). Wing ornaments and so forth can be added optionally.




* * *

Simple as all this still is----it may not be simple enough. A standing bird has fundamentally four points, even when its wings are slightly split. A four-point model ought to designable reasonably from a bird-base. And if it’s a bird base, then the principle of continuous complexity ought to apply, and feet can be point-split if one cares to, a beak opened, and so forth, all from essentially the same beginnings, and stopping whenever one has had enough.

Can this be done?

Stay tuned.

P

Sink or Swim

The awful thing about this origami business is that it keeps changing. You can never rest on your laurels. At any given moment, somebody, somewhere is doing something mind-boggling, or worse, is busy outpacing you at the very thing you once most prided yourself in. I shudder to think what will happen if Ronald Koh ever comes out with a book—having seen a few of his Fish, the best in the world, and knowing something of the design problems involved: won’t a book will make it clear he’s one of the foremost animal designers of our time?

But there is no need for dreadful anticipations. As we speak, out there on the edge of the universe, in Calgary, Canada, Roman Diaz is plugging away at his Birds: carrying the study of avian origami to what I think everyone will recognize as new heights. His bird from the post before last (Nov 1 2006) is not so much a homage to Michael LaFosse’s Cardinal as a rival to it, in elegance of straight-line form and color (if not in simplicity of design), something I would scarcely have imagined possible. And in the ‘Calandria’ of the last post (Nov 9) there is more improvement still: this time on the rounded form of the bird. --All of which personally would be an unmitigated joy were it not for the fact I’d staked out some of this field for myself, once upon a time. I am not yet ready to cede at least partial ownership of it. Not without a fight anyway. I don’t mind losing but not quite so easily...

Let us pick nits. Roman says, if my feeble Spanish is getting it right: (a) very many birds in origami are indeed made from the Bird Base; and (b) without using High Technology, a standing bird with wings folded on its back will not show two distinct wings, but only one conjoined surface, if made from the Bird Base or any of the other traditional bases.

As to (a): I’m not at all sure this is factually true. We may have to consult the Origami Database (supposing it somewhere contains the useful category of bases a model was designed from) to see how many birds really are made from the Bird Base as a share of the total. The term itself certainly did not originate from any such preponderance of designs, any more than the ‘Fish Base’ is so called because most or even many fish derive from it (of that I’m surer: they don’t). Presumably only one bird ever gave rise to the term ‘Bird Base’—the Crane. Historians are of course invited to do their stuff here.




When I set out last year to show an assortment of ‘Bird-Based birds’ of my own design it was not because this seemed an especially natural or widespread thing for model-makers to do; the point was rather to show that there was life in this tired old base still, and that models of considerable purity and power can be made from familiar beginnings and relatively low technologies. (Dare to be ridiculously simple, stupid and obvious, my motto seems to be.) I was annoyed in particular by the birds Robert Lang had displayed at Barcelona (2005), which took over 50 steps to make; a few trials over the years had suggested that slightly simpler, but just as effective birds ought to be makeable in no more than 10 to 15 steps--or say 20 if you point-split feet, which isn’t always an improvement.

But having considered the matter further, it now seems to me that the Bird Base really is a natural beginning for birds, standing ones especially—even ones with substantial amounts of detail. That’s because it puts the points in all the right places and leaves them pretty much independent. If you want to add details that cost you limb length (e.g. point-split feet), you can always compensate by shortening the other elements proportionately (ideally adding detail there too). This then yields a design virtue I try to get from all of my own origami: something we may call ‘continuous-complexifyability.’ (Ugh. Ugh!) That is: a design should yield good enough results in its most simple format, but also be able to sustain gradual increments of complexity or detail, if that’s desired, without modifying the superstructure. The ideal would be for Roman’s useful ‘progression of bird complexity’ illustration to be the literal truth about adding details to the same model (or barring that, to the same concept). With a Bird Base, that is almost possible.

As to (b), the point about folded separate wings: As a generalization that may be true. But it also depends on what you consider to be the ‘Traditional Bases’ and what you take to be ‘High Technology’. (OK, so Roman did not use this term.)


For instance, here’s a picture of an actual 1987 model, the ‘Fat Pigeon’. It’s from a Stretched Blintzed Bird-Base. Does that count as a “traditional base? The technology is pretty ‘traditional’ too, i.e. practically obsolete, though in ‘87 it was state-of-the-art.

For the record, about six months ago I simplified this model (abandoning legs altogether) and made a version from a plain old stretched Bird Base. Here it is. This modification follows two design principles, the first one tried and true—“KISS”, or, ‘Keep It Simple, Stupid’—the second more theoretical and unproven: “POETIC”, or ‘Put Opposite Elements Together, Idiot, in Combinations.’ (yeah I just made this up.) Here the ‘combination’ is of 3D/rounded form with 2D and even 1-D elements--the paper’s cut edge, made visible.


And what about the Bird-Frog Base? That’s at least hybrid-traditional, and is getting more traditional by the minute. You can make a split-tail (not split wing) bird from it easily enough. I’ve also made a Whooping crane (1988) from it and, following the principle of continuous complexifyability (…), just adding toes, a Heron (2005). Its close cousin is the Crane designed by Daniel Naranjo and further developed by Roman Diaz himself—which is from a Waterbomb base, and so unquestionably “traditional”. The wings in all these cranes can be folded up in exactly the way actual cranes do it, creating a two-winged back, though for origami this would clearly be a waste.

But it’s true. If you add just the teensiest graft to a plain old bird base you can get away with a lot more. In particular you can not only get the wings on the back to split but send the tail shooting up between them, which in my lexicon of bird emoticons, is the very expression of Joy.

Thus far I’ve been discussing history, some of it ancient history. Hopefully next time I’ll have some new things to show.

So: am I holding my own? What do you think?