I went to a talk last week on protein folding, given by one of the College’s chemistry profs. I was delighted to find that there is a mechanism for correcting folding sequences that go wrong. Any folder will recognize this situation immediately: you get almost to the end and see flaps sticking out in all the wrong places. So you curse a little and then unfold back to the part that you knew was right and start over. Some might say, ah, evidence of intelligent design! Well, maybe — intelligent design is certainly a plausible theory, but it presupposes that humans would be intelligent enough to recognize it if they saw it. There exists nowhere any evidence at all for that. Puny humans. Howsobeit, it is evidence of good design and even Morbo the Annihillator would appreciate that.

This is a ten-sided yin-yang globe, a modular kirigami model I designed for a friend to use in a gift exchange for the 10th Gathering for Gardner. Martin Gardner wrote the Mathematical Games section in Scientific American magazine for many years and had a big influence on a lot of folks, paperfolders not excepted. My brothers and I first learned of Samuel Randlett’s books from one of Gardner’s columns. My friend, Norton Starr, had four hundred of these models cut and scored at a local press and will be sending them out to his cohort shortly. This post contains the directions on how to assemble the model.

(For those of you who do not belong to the G4G group, there is no reason to feel disenfranchised — here is the template in PDF and you have only to print it out on two different colors of light cardstock or heavy paper. You then can cut the pieces out by hand — a little tedious, I admit — and assemble as described below.)

Step One -- Carefully punch out the pieces from the templates.

Step Two -- Make sure you have cleared all the paper from the inside of the hooks.

Step Three -- Fold in on the indentations: not all the way, just partially as shown.

Step Four -- Flip pieces over so that they resemble integral symbols.

Step Five -- Place a white unit on the table and then a purple unit on top of it, rotated approximately 36 degrees counterclockwise. Note how the hooks overlap.

Step Six -- Add a white unit, rotated approximately 36 degrees counterclockwise from the purple unit. Continue alternating units until all ten are in a star formation. (Don't worry about being exact about the angles -- the model will self-correct when assembled.)

Step Seven -- This is all ten units assembled. Once you have this, flip the model over, so that the swirling circleStep Eight -- Pull and curve up a white unit so that the top is about 3½ inches (10cm) above the intersection.

Step Eight -- Pull and curve up a white unit so that the top is about 3½ inches (10cm) above the intersection.

Step Nine -- Pull and curve up the purple unit to the left over the white unit. Hook the ends.

Step Ten -- Pull and curve up the white unit to the left and hook in the same manner. Continue around the model until you have hooked all ten units.

Step Eleven -- Hooking the last unit. When you release the disk, the model will compress at the equator and even out the angles.

Origami isn’t only an art form, practiced by thousands worldwide, it’s also an Australian jazz trio. And they have an album coming out.

This album comes in two forms: the now traditional digital download and as a physical CD with an origami CD cover. A rather attractive model, we think, one that may be familiar to our readers.

The packaging for the physical CD has been produced on a sort of pre-industrial basis — the paper was printed and scored at a print shop, but then folded by hand by saxophonist, Adam Simmons and others in his circle. The paper is Teslin, a synthetic stock, used mainly for ID cards — not so easy to fold, but quite resistant to tearing. Obviously, a limited release (Adam mentioned that he’d made several hundred) and bound to become a collector’s item in short order.

The music, like the packaging, is intricate in its arrangements, pushing gently at the envelope of its medium. Highly recommended to your attention.

The second method here is one of embedded self-referential directions, a web analog of genetic information. Say this model is left somewhere public, a cafe or bar or bus station, and some geeky boy walks by. The QR code attracts his interest, he photographs the code with his smart phone and bam! the phone comes up with the page you’re reading with handy links to the diagrams and and special paper. Very meta. The geek prints it out and either folds it or finds some more knowledgeable geek in his geeky crowd to fold it. Thus is the circle of life completed, only to begin again when the geeky crowd runs off to the next flash mob happening, leaving behind the wily QR code bug, where it sits on the table, quietly contemplating its own intentionality.

Metatextual reproduction is discouraged or forbidden in some jurisdictions: please consult your local laws before propagating the QR code bug.

I was just admiring the calendars on the CDO site and of course, admiration leads to emulation. Being a cube, this is just a six month calendar, but when July comes, you can open it up, reverse all the folds and there are the next six, ready to go. June and December aren’t the easiest to read, I grant you, but folding accuracy on this scale is problematic.

The type here is Igino Marini‘s wonderful IM Fell Double Pica PRO, which dwells in this world under an SIL Open Font License.

Crease pattern here (the curiously versatile jasmine tea cube) and a PDF of the calendar here — print the latter back-to-back. (Schiena contro schiena, forse).

While I’m here, let me also point you at a nice video, posted by Leyla Torres, which provides a slower, more in-depth view of how to collapse the Smart Waterbomb.

About a year ago, I read a book on Japanese temple mathematics that I found in the local libraries. Well, I didn’t read it completely — there was a great deal of it I couldn’t follow. But the pictures were beautiful and what I understood, I enjoyed. During the Edo period, that is, after the Japanese had been exposed to Dutch traders, but before they’d met the Americans, there was something of a renaissance in Japanese math. Part of it was that mathematicians would make wooden tablets with strange geometry puzzles on them, sangaku, and hang them in Shinto temples throughout the land. Other visiting math-heads would attach solutions to the problems. This was once a common practice, but the modernization that followed the opening to the West led to its decline and eventual abandonment. Most of the tablets were lost, but those that survived are now museum pieces and carefully conserved. They’re beautiful to look at — some of them resemble crease patterns. (That’s where I came in.)

It’s not really clear to me why temples — you’d think schools would be a more likely place for this activity. (You remember how your high school math teacher would post puzzles on his bulletin board?) Were the Japanese scholars trying to amuse the gods with their puzzles? Were the tablets thank-offerings for a moment of mathematical clarity? The book never quite satisfied me on that point.

So, Saturday, I had this idea that I wanted to make an octahedral box. There are roughly a gazillion octahedral origami boxes, but I wanted mine a little different, with a pockets and an iris closure on one side. I thought about where I wanted things to go, drew a crease pattern and made the box — it worked well and I was satisfied with the results.

I figured I’d do the folding sequence later — it’s usually easier, after the fact.

Then Daniel Kwan innocently asked me if there was an elegant way to get to the grid for the model. I said, sure, no problem, and quickly discovered it was a much more complicated problem than I had thought. The center triangle is concentric with the circle and that sounds as if it should be pretty simple, but it’s not foldable in the way we usually do triangular grids. After a couple days, I came up with a triangle I could fold that would give me the right angles, but by then Daniel and Andrew Hudson were already making discoveries of their own.

Daniel came up with a very nice folding sequence:

And this works very well, though it might need some fleshing out for the general folding public.

Andrew noticed that the grid not only uses a 6-pointed star, but also divides the circle by ten:

And then he generalized, proved the idea and started riffing upon it:

Andrew wonders “how much we’re missing by restricting ourselves to squares.” A very great deal, I should imagine.

And all of this is good stuff — all of this can be used elsewhere, in tessellations, representational works, whatever. I would encourage you the folding public, to try it out. I was, as I said, satisfied with my box, but rather better satisfied with the conversation that followed it.

Maybe the Japanese mathematicians hung their puzzles in the temples because they were there and open to the public, a place travelers would pass through and where locals would visit regularly. Maybe in Edo Japan, the temples were not just places of devotion, but also served as a marketplace for ideas. Sort of like, you know, using a photo site for the exchange of origami techniques.

Himanshu was asking the other day about how curve folds were made and I did what I usually do, respond with a text description of what I think I’m doing when I fold curves. But I’m always aware, this is not a very satisfactory way to explain it.

The Smart Waterbomb is a simple model, which is not to say easy. A thing may be both simple and difficult. This model has 12 folds in it and no reverses — that’s pretty not complex. And it holds together well. When I try out a new paper, this is one model I always fold, to see how the paper will support a curve. It’s easy to memorize the sequence of folds.

Anyway, I’ve made a video of it, so that you at home can fold along with me:

It probably bears mentioning that Californian folder, Chris Palmer, made a model that bore some similarity to this one, some years previous. Whenever you enclose space with radial symmetry, you will have this issue. As we often say, when we’re affecting wisdom, there’s nothing new under the sun. But that doesn’t mean we can’t share new ways of refracting the light.

Who:
Christiane Bettens, Christine Pape and Philip Chapman-Bell, the administrators of the Origami for the People flickr group…

What:
…cordially invite you to participate in our first annual Feast of All Fools Challenge.

Where:
The Origami for the People group page.

When:
From now until 23:59 April 1, 2010, Greenwich Mean Time.

Why:
Really, that’s very complicated. Let us say for the glory of it and leave it at that.

How:
In spite of the timing, there is no special theme to this challenge. Origami for the People is a group that encourages and documents the unsanctioned placement of origami in the public sphere. (That is, we leave models in public without asking permission first.) We value the aptness and/or the unlikeliness of the model to the placement.

We require geotagging on the photos submitted to the group, so that we can view the results on a map or on Google Earth. If you’ve never geotagged before, there’s a little tutorial on how to do it — it’s easy.

In order to enter, you should: 1) geotag your photo; 2) attach the tag OPPchallenge2010; 3) and submit it to the group. (You have to have a flickr account and join the group to submit — it’s fine, you can quit later if you don’t like it.)

There is a limit of three entries per person, so choose your installations with care.

Prize:
The winning entry will become the group avatar until the next challenge. If that’s not glory, we don’t know what is.

Special bonus challenge:
A special, as-yet-undetermined prize will be awarded for the first verifiable photo of an origami penguin in Antarctica or of an origami polar bear above the Arctic circle. (Id est, no Photoshop — you have to be there in the flesh to take the photo.)

The administrators encourage you to spread the word — please feel free to translate this challenge and repost to other forums and/or mailing lists.

(And since you read this far, you can have some sketches I made towards diagramming the model above.)

This is the Victoria and Albert Museum in South Kensington, London, UK. I can’t say I know much about it, but you can read up on it by clicking the photo above — it will take you to the Wikipedia article. I mention it here because someone who works there recently blogged about this blog and it caught my eye. Mainly, because the author mentions me in the same sentence as Robert Lang, which almost never happens. In fact, there is only one other documented occurrence of it ever happening: a year and some back, through a series of improbable accidents, I was having lunch with a group of famous folders in a ramen restaurant in San Francisco’s Japantown. Famous folder, Joseph Wu leaned across the table and stage-whispered, “Philip, your elbow is in Robert’s soup — it’s considered very rude.” And I thought, “Man, the Japanese got rules for everything.” But as the soup was uncomfortably hot, I did move my elbow and quickly made small talk, to cover my étourderie. Well, that aside, the blog entry is on design and how drawing your ideas affects the finished product. Interesting stuff, recommended to your attention.

Speaking of finished product, yesterday, I folded this, the Plausible Box, on the bus, while chatting with an old schoolmate about what we’d been up to the last twenty years or so. Martha said, “I’ve seen you folding on the bus — you keep folding things, then take them all apart and fold them again.” And I said, “Yeah, that’s my design method. Take it apart, reconfigure, recollapse. Eventually, it will work.” This one works for me. Give it a try — it’s based on the 3×3 tato. Here’s a crease pattern.

Our subscribers by email will be seeing a whole lot of nothing, here. But if you click on the title link, it will bring you to this post and some cool video instructions for the Iso-Area Double Masu.

Which is a variation on Toshikazu Kawasaki’s Iso-area Cube from Kasahara’s and Takahama’s Origami for the Connoisseur. Not that this model is in that book or that Kawasaki ever folded it. It is, to my knowledge and belief, a new variation. I deem it sufficiently different, both in shape and in folding method, to qualify for status as its own model. Your mileage may vary.