Tuesday, October 26, 2010

Toward a Lineless Origami

It's not entirely impossible as a goal, as these experiments show.
But how far can this be taken?


Posting these before I ruin her face from overwork, as I surely will. You can still see the smoothness of the paper I am trying to preserve. --S.


Added Nov. 17. Here she is at a later stage.

And finished:

Sunday, October 10, 2010


Wet-folded from an uncut rectangle of Canson paper.

In recent years most of my face-work has been from foil-backed paper (and in the 1980s it was from pure foil), but I've always wanted to see which of the techniques work also with pure paper. I'm slowly learning how to wet-fold, so here are some preliminary results.


Monday, June 14, 2010

Embryology (1)

It is sometimes said that the process by which an origami animal is made resembles that which real living organisms go through—that origami yields up a sort of “parallel embryology”. This is a charming metaphor, but just what does it mean, and how far can it be taken?

Let’s start with one sense in which this is not an analogy at all, but a literal description. There is a key stage that all animals go through as their forms develop, that involves folding. This is the stage of gastrulation (and also the next stage after it, neurulation). That is when the embryo changes from an essentially 2D shape to an essentially 3D one. The egg has been fertilized, several cell-divisions have taken place, and now there is a fluid-filled ball (called the blastula) of up to several thousand cells, its wall one or two cells thick. Paperfolders will recognize what next happens—invagination at a point on the sphere, then a line, and finally a circle—as a sink: material from the outside is pushed inward, to form a second internal layer. The part that stays outside is called the ectoderm (‘outer skin’); the part that moves inside as a continuous sheet is called the endoderm (‘inner skin’); and in some species (like our own) as the paper is pulled over the lip, bits of it break off (ingress) to rejoin inside as a third layer, the mesoderm (‘middle skin’). Out of these two or three skins, all of the animal’s body parts will be made.

The next stage, neurulation, is even more visibly origami-like. The gash or the circle through which the material has been stuffed closes to a point: drawn shut like a purse-string. (This will be the anus.) One surface of the elongated spheroid flattens; a fold-line appears on it, a single meridian on the spheroid. To either side, ridges rise (mountain fold-valley-fold-mountain-fold) and then start to join. Where they join, the cells intercalate (almost: zig-zag folds on either side, slotting into each other); this will be the animal’s nerve-cord, very soon its spine. Meanwhile at the far end of the spheroid (now also the top of the nerve-cord) the valley is wider, so as it closes it curls up and bulges appear. The head with the brain, visibly, begins to form.

Of course it is more complicated than this. Gastrulation happens very differently in different species (though with a similar end-result and similar genetic basis in all, indicating an ancestrally unitary process). So the above description fits a frog better than it does, say, a chicken (where, instead of a round sphere you start with a flattened one: a pancake perched on top of an egg yolk.) Mesoderm formation, where you tear off bits of paper and stuff them inside, is nowhere origami-like. A huge amount of cell-signaling goes on during gastrulation, with cells being ‘position stamped’ as the layers slide and pass under each other, information that will be crucial in later developmental stages: that too can’t occur in a dumb mechanical process like origami. Cells are also constantly dividing and the sheets are expanding, which is quite different from the unstretchable surface that paper presents. And of course the motions here are guided entirely by the cells themselves, with no outside fingers (or even chaperones) doing the pushing and pulling. Nevertheless and despite all of that, form creation at this stage is primarily an issue of folding sheets, the developing embryo obeying constraints and realizing opportunities for regularity and efficiency that folding alone can provide. And so in a very meaningful sense, all animals, three-dimensional, bony, keratinous and full-blooded as they turn out in the end, are products of origami.

Origami people who have read this far—you’re in for a treat. Have a look at this video of a frog embryo as it undergoes gastrulation and neurulation.

That’s it—that’s when the magic is done.

Origami—purist origami from a square—is still largely about making animals, for all the sailboats, jackknives, racing cars there are in the folded world, or plants for that matter. And here’s Why. (One fraction of why.) The smooth square you start with—has rotational symmetry, or at least you can spin it 90 degrees about its center indefinitely without changing it, and flip it over and do the same. But then you fold one edge to another, and look what happens. You’ve created a spine in the sheet, first and foremost—a region with a different texture and thickness, that is also an axis, and also a hinge. You’ve given up much of the initial symmetry, though there is still some left; but in particular you've set up a frame for a bilaterally symmetrical form. You’ve brought corners into alignment, pairwise, with pairs separated. Edges have been transformed: where before they were equal, there are now three different kinds. All this in a single step! You will be hard-pressed to make any other move later on that introduces so many new qualities to the developing form (though if you’re worth your salt as a designer, you will go on trying to find such.)

No matter. The basic shape after that first fold is already more animal-like—because of the spine, because of the bilateral symmetry it imposes, and because of the two separated pairs of ‘legs’. There is no real head or real tail unfortunately, only a marker of sorts where they should go. Alternatively, if, as in most origami animals (so I would guess), the first, spine-forming fold is along the diagonal, then you will have a head and tail already positioned and the legs will have to be figured out later. You will frown at that single pair of corners of the triangles—it’s the wrong number and in the wrong location, centered rather than spread near the head and the tail. This problem can be dealt with, of course, but everything costs.

Now let’s look back at the embryology case. The flattening of the surface (as the material stuffed inside crawls up one inside face of the spheroid) and the stage of neurulation—fold-forming the chord /spine—is exactly analogous to the ‘first fold’ in origami. That is, this is the move that marks and positions the physical spine (not via a single mountain-fold but by a mountain-valley-mountain; that’s what it takes both to get a channel and to build up thickness). This is also the move that finalizes the imposition of bilateral symmetry on the developing animal: henceforth there will be a left side and a right side. There wasn’t quite before. One end now will give material for the head and one for the tail—just as with the square. Top and bottom of the animal—in the case of the square this has yet to be decided (things can still be turned inside out); in the case of the embryo, since the chord-fold is on one face of a temporarily flattened sphere, that’s the top and whatever’s on the other side becomes the bottom.

So at least some of the crucial moves, purposes and effects are VERY similar as between origami and biology. These beginnings and what happens next have lingering implications for the shape of both real and paperfolded animals, and the resemblance is retained.

I know that this is not really what people have in mind when invoking the origami-as-embryology metaphor . Presumably the analogy is more innocent: you start with a simple, pure form, the square (as pure a shape as the egg); manipulate it, differentiate parts, move them around, progressively add detail, and finally round out the shape and breathe it into life---all in a linear sequence that can be repeated more or less identically by any folder given the same diagrams/DNA. What could be more lifelike?

I’ll come back to this ‘innocent’ concept in a later post. For now though, we can chalk this up as one of those rare cases where a metaphor’s validity outstrips it’s intent.


Thursday, June 03, 2010


macaques allogrooming

I once suggested in jest that the reason origami is so successful in calming people and bringing out conciliatory instincts is that humans are basically primates, and a calming activity that used to take up a lot of time in our social life--allogrooming--disappeared without a trace once we lost our body hair. There’s been no good replacement ever since, and origami is the first thing in a while that even comes close. All that intense concentration and fussing with fingers in a social context over something small that needs puzzling out. --Of course no one was really meant to take this sort of idea seriously... least of all me…

snagged from Dave Brill's Freising photoset. Thanks Dave!

Monday, April 26, 2010


It’s not just in the weird paperfolding that I do, but also in the most conventional sort of technical origami, that a principle of “non-interference” applies. After all, those individual toenails or flight feathers one is showing off can't be allowed to cause trouble for the rest of the bird, can they? I am something of an extremist with this principle, and often try obstinately to squeeze out as many features as possible in the middle of the sheet while leaving the edges entirely unblemished.



Wednesday, February 17, 2010


Down pending revisions (may be a while). For now, enjoy this oldie

Tuesday, February 16, 2010


If the Internet hasn't completely frazzled your brain and fragmented your attention-span, there’s a 100-page book, written about 100 years ago, that I’d like you to read.

It is Emanuel Loewy’s “The Rendering of Nature in Early Greek Art”. You can find it here.

It gives a lot to think about; some of which strangely enough bears also on origami.
Go ahead and read it and I’ll get back to you in a few weeks.