Satoshi Kamiya’s Feet Thing (And More Origami Showerthoughts)

by Marcus

More origami showerthoughts for you all! Random musings, random questions, and even some genuinely interesting theories about origami towards the end.

 

We Teach The Petal Fold Wrong

The petal fold really doesn’t need three precreases. It only needs two—and I’ll demonstrate why. The traditional precrease that I’ve been seeing in origami books for years looks like this:

 

One on each side to make a kite, and one folding the thick point down. But here’s the thing: you don’t actually need to fold the thick point down! If you fold the other four creases, that one forms by itself because of the alignment of the creases on the sides:

 

I think this helps with two things. First, it teaches people about what I like to call “ghost folds,” folds whose positions are given to you even if they haven’t physically shown up yet. Second, this breaks the petal fold into much simpler components—two reverse folds and a valley fold—and that’s an essential skill if you want to get better at origami. I’ve already started leaving out the third precrease when I teach the bird base to people, and I think everyone else would be wise to do it too.

 

Asymmetry Isn’t Actually Hard

Because what’s hard is partial asymmetry. Most asymmetrical models (such as hermit crabs or barbarians) require asymmetry in only one part of their bodies. Everything else still has to be symmetrical. This is exactly what makes asymmetrical models difficult to design: the highly symmetric square makes it all too easy for a single asymmetric section to throw off everything else in a model. If a design is asymmetric all the way down to its core, things become surprisingly manageable. (See Satoshi Kamiya’s “Venus Comb Shell” and “Wizard” designs for examples of this.) But I hate the knee-jerk idea that “asymmetry is hard,” because it’s nothing more than a limitation of wording. If we can get rid of it, a block on our imagination is lifted, and the potential for structural innovation in origami will become endless.

 

I Hate Big Sheets (And I Cannot Lie)

Perhaps this is unsurprising coming from the guy who made every Robert Lang insect out of three-inch tissue, but I feel like using really big sheets of paper for complex models is kind of boring. Even if they make models a lot easier to fold precisely and without tearing, there’s an element of risk that’s gone when you do that. And that takes away so much fun! I love the challenge of folding things from paper that’s just a tad too small, working with the resources you have instead of going out to buy more.

 

Satoshi Kamiya, Origami’s Quentin Tarantino

Whenever Satoshi Kamiya makes an animal, he always does something very interesting when shaping its feet. Specifically: the angle at the tip of a foot is always blunter than 22.5°, even if the flap leading up to it ended with that angle to begin with. Take a look at his Protoceratops, for instance:

 

Or his model of Sleipnir, the 8-legged horse:

 

Even arthropods have something similar going on: in a leg flap with an angle of 11.25° in the Fiddler Crab, the ends are widened to an angle of 22.5°.

 

The main exception to this shaping rule is actually birds, because their feet are so pointy anyway:

 

But in every other case, particularly mammals and reptiles, he makes sure to shape the feet like this, and he’s been doing it since extremely early in his career. This is a really small detail, but it makes a model feel so much more real and so much less like an “origamified” animal. Go ahead and copy him!

 

With Further Apologies (but not really) to Akira Yoshizawa

I’ve been thinking a lot about this quote by the folder Philip Shen, from a 1965 article in The Origamian:

“..we should not be so fascinated with animal forms, because they sometimes impose too great a limit on the imagination…. Maybe we should try abstract forms or geometric shapes more often. From new geometric shapes we can then proceed to other more easily visualized forms. All basic forms are geometrical. I believe it is the geometrical forms that are the logical basis for further, creative development.”

I’ve seen similar things said by Paul Jackson and Jeremy Shafer, two modern-day folders. They prefer making abstract models out of a feeling that “realism” is overdone and cliché. But I was surprised to see the sentiment pop up so early in folding history.

In Yoshizawa: A Retrospective, I asked why Yoshizawa enjoyed the animal subject so much, and I came up with this:

“The main use of folding at the time was as a children’s toy, thanks to the influence of Friedrich Froebel and the Japanese kindergarten system (discussed previously in Origami and Orientalism). Froebelian folding was largely geometric, based around various properties of the square, and Yoshizawa broke away from this paradigm.… He has attained a status similar to that of Beethoven, breaking out of the Classical tradition and paving the way for an entirely new era of origami expression.”

But I’m inclined to rethink this statement. Yoshizawa did not create a new style like I implied in that essay. Instead, origami styles can be thought of like a pendulum, swinging back and forth between abstraction and realism. The kinds of expression that are popular are always changing and always have been changing. Yoshizawa was not the beginning of an era nor the end of a previous one, but merely one place in the middle of a cycle. And I guess that’s one more reason he wasn’t actually as significant as everyone says he was. Oh well.

 

When did origami books start putting a little description of the subject at the beginning of the diagrams?

The earliest book to do this, to my knowledge, is African Animals in Origami by John Montroll (1993). In that book, each animal gets a small description, with biological information like its diet and geographical range. Other books, like Jun Maekawa’s Genuine Origami (2008), have details about the geometry of the models. Nowadays, it’s just the norm to put a little information about either the subject of the design or the design itself. But when did that norm really take hold? I’d love to do more research, but I don’t have time for a big project like that at the moment.

 

When did origami books stop putting the diagonals in the first drawing as if you’ve already made them?

Honestly, why did they ever do it in the first place? There are certainly more egregious mistakes one can make when writing diagrams, but this one has always grinded my gears. I DON’T NEED TO START STEP 1 AND THEN GO BACK AND REALIZE I HAD TO DO ALL THESE EXTRA CREASES BEFORE STEP 1. And they’re never given with parity indications, so you have no idea if they’re meant to be mountains or valleys. I’m glad this eventually fell out of fashion—it’s pretty obvious that modern origami books have much higher standards for clarity—but again, when did that become a norm? So many questions, so little research time…

 

Origami: An Art and… a Science?

I’m a scientist at heart. That’s a big part of how I view origami and life in general. I’m also aware of the many great uses of origami in science and engineering, from solar panels to surgical stents. But for some reason, I don’t like writing about origami in science. I’ve literally never done it on this blog. Why doesn’t it appeal to me? I have no clue. I’m a very interdisciplinary person, and I think science and art have a lot to learn from each other. But maybe sometimes some things should just be separate—and that’s totally okay.

 

How Not to Make a Barosaurus

Some time ago, I came across this picture of Satoshi Kamiya’s Barosaurus in a paper review, folded by a then 14-year-old Ynon Toledano, and I laughed out loud the moment I saw it:

 

Some advice for young folders: Please, PLEASE, never do this. I used to do the exact same thing when I was a teenager, and I understand the temptation just as much as anyone. But it will be so much better for your origami if you understand where to stop shaping. Restraint is one of the most valuable skills you can have when trying to make a truly artistic model, and I would have rather learned it sooner than later.

 

Third-Wave Origami: A Theory

Some time ago, I learned about the three waves of coffee, which was itself a categorization inspired by the three waves of feminism. Essentially, the term describes an increasing focus on coffee quality (temperature of roasting, source of the beans, etc.) over the years, with different waves marked by specific events in coffee culture history. I soon began thinking: could a similar term describe origami?

In first-wave origami, most designs were simple, derived from the Classic Bases, and fairly abstract and geometric. The folders of this era—Miguel de Unamuno in Spain, Michio Uchiyama and Isao Honda in Japan, and several others—started making (and recording) their own designs and laying the foundations of the art. At this point, origami was still largely a children’s toy, and most models could easily fit into a quasi-Froebelian elementary school setting. This changed in the second wave, starting around the 1950s and 1960s, which saw an increase in complexity and a greater effort at realism. Folders like Neal Elias, George Rhoades, and Fred Rohm began making specific subjects and exploring new bases to fold models from. Origami societies like the Friends of the Origami Center of America (now OrigamiUSA) began to pop up, connecting passionate folders and distributing the latest designs. Yoshizawa, who had started folding some time into the first wave, gained much of his popularity in the second. Early paper innovations such as long rectangles and foil made many of these new designs possible. The end of the second wave would see designers like Robert Lang and John Montroll start to stretch the technical possibilities of origami. In doing so, they kicked off the third wave, which resulted in an explosion of complexity in origami that continues to the present day. Beginning in the 1990s, mathematical design strategies fully supplanted the Classic Bases by allowing the creation of custom structures for any model. These included circle packing and later box pleating. The Japan Origami Academic Society (JOAS) was formed in this wave and would become a nexus of innovation in origami design. Cutting and multi-sheet models, common in the first and even second waves, were slowly phased out as they were no longer needed to create realistic models. Shaping became a priority as well, and curved folds gained increasing use in the designs of people like Michael LaFosse and Eric Joisel. These trends would all continue into present-day origami, which is still iterating on these developments.

Now, the above theory is a dramatic oversimplification, and also leaves a lot of questions about origami unanswered. Are we still in the third wave? Is what we have right now a fourth wave? What about modular origami, which I didn’t mention at all? What about the different folding practices between different countries? All of this should be discussed. But I am happy enough to bring up this framework and leave it for others to critique.