Monday, December 25, 2006


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".

Sunday, December 17, 2006


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]

Friday, December 08, 2006

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.

Saturday, December 02, 2006