The Origami Forum

I've had ideas that are simple in concept, but impossible to fold due to paper thickness. In my case these patterns tend to involve repeated folding steps, but surely there are designs discarded due to the limitations of paper that are not recursive.

I've shared some of my recursive crease patterns before here and there, but it occurred to me that I'd love to hear of what others have concocted even if it only exists in the aether. So if you'd care to describe your designs below, I'd be very happy to read about them. Crease patterns, written descriptions, 3D models of what it would look like given impossibly thin paper and an eternity are all welcome.

To start things off, the most frustrating recursive model I've come up with* is a diamond perpendicular to a plane:

Folded, two levels


Crease pattern, many levels


What it would look like with infinitesimally thin paper and a LOT of time


In theory, you can narrow the base of the diamond (where it touches the rest of the paper) to a point. Sadly, each time you half the size of the connecting corner, you double (maybe more?) the number of layers.

Folded for one iteration it looks pretty good. Folded for two, not so much. Anything beyond that tends to be a disaster.

Because these diamonds can be tessellated, I was hoping to do many of them from one sheet of paper, narrow the connecting corner and fold cranes out of them Sadly, it is not to be.

As a side note, the faces of the diamond are unfolded. So this could, in a perfect world, be made into a fractal (diamonds on diamonds on diamonds...) that was also tessellated.

* I've found out that Maekawa's Turkey has a similar structure. So independently invented, but not an original, I'm afraid.

If you have 'infinite' resources, there are options.
1. Thin tissue-paper, scored with a laser might give you a few more iterations. This is what Robert Lang has done ... Of course, he's a laser physicist with a few more resources.
2. Erik Demaine is a professor that explores math issues related to folding Origami, might be worth Googling.
3. Independently, folks like Kamiya Satochi, Tadashi Mori, and Brian Chan (MIT?) work with very detailed CPs, that may provide hints for detailed tessellations.
4. In addition to making terrific Origami videos, as well as terrific kids , Sara Adams is interested in tessellations ... and she might have suggestions for folding techniques.

I suggest that you create some more challenging CPs with cranes, and then put the CPs out as a challenge to fold They might even be OK to submit to the Christmas Book ...

HankSimon wrote:If you have 'infinite' resources, there are options.

Thanks for the reply. While I don't have infinite resources quite yet, I like the options you listed I do in fact have one other crane-related model that would benefit greatly from infinitesimal paper:



It might be a bit hard to make out, but it is four cranes. The base (the black parts that look a bit like stilts) can be made arbitrarily thin, again, in a ideal world.

I also have a pattern for making connected cranes out of long rectangles of paper, but that one is quite feasible with normal paper In any event, perhaps I'll ask around and see if anyone can suggest something clever.

Just out of curiosity what is the Christmas Book?

Christmas Book: viewtopic.php?f=12&t=12714&hilit=christmas

If that link doesn't work, search the Forum for Christmas Origami Book 2014 . It is an annual ebook assembled by Anna (I believe), by collecting original unpublished Origami diagrams from volunteers. Anyone that submits, gets a copy ... and only submitters get a copy. And if you submit more diagrams, you get a previous year Christmas Book.

Unfortunately, I do not design, so I have never seen these marvelous books

HankSimon wrote:Unfortunately, I do not design, so I have never seen these marvelous books

That's a pity. You might want to reconsider and try yourself at designing.

@Cadix:
Your model reminds me a bit on Jeremy Shafer's Star of Peace that can be found in his first book "Origami to Astonish and Amuse".
A picture can be found here: http://www.barf.cc/jeremy/origami/BOOK/ ... peace.html
About the connected cranes from rectangle, I remember some pictures of a man who made a thousand cranes from a huge paper roll, where the cranes were connected on their wings. Unfortunately I fear the pictures are no longer available.
I also remember having seen a crease pattern for tessellated cranes where the author stated it would theoretically work, but he wasn't able to fold it, but I can't remember where it was.
Anyway good luck with your project.

I think my roommate Josh was right: I may be one of few people who keeps track of, and has an interest in, their "failures". I was hoping to find some company in that respect

@origami_8 I haven't gotten around to getting in touch with/googling the people you mentioned. But I did have a thought...

It occurs to me that the thickness of the base (the number of layers where the diamond reaches the rest of the paper) stays the same regardless of the size of the diamond. I wonder, if I fold it out of much larger paper, will the thickness be less of a problem?

I'm going to try it out, but maybe you have a thought?

You have lots of company, as far as failures.... Many of the old folders keep a 'trash can' containing incomplete models or designs, which they return to periodically, as they make progress folding other models.

In my own case, it took me a couple of years to finally learn how to fold the wheels for Mooser's Train, and a few months to understand the diagrams for the base used to hold Crawford's Three-Masted Ship.

I'm misquoting, but the gist is that Robert Lang related that Akira Yoshizawa had said that it took him 25 years to be happy with the design of an origami Swan (?) ... And, that Lang himself had become aware that he continued to re-visit one of his designs over a couple of decades ...

I believe that Quentin Trollip and Seth Friedman may have had similar experiences on their way to becoming Origami Masters.

You're in good company

Well, the thickness doesn't change and will therefore always be an issue, even if you had access to infinitely large paper. On a small scale it might help though to take a bigger paper. Working with thinner paper however is more advisable.
In the end what you need to do is device a molecule that you can tessellate. Some people already did some design studies in this area (but not for cranes in specific), for example Andrew Hudson and Natan López. Tomoko Fuse did some interesting work on tessellating with many layers.

origami_8 wrote: I also remember having seen a crease pattern for tessellated cranes where the author stated it would theoretically work, but he wasn't able to fold it, but I can't remember where it was.

Are you thinking of Robert J. Lang's one in Origami Design Secrets (Second Edition) pages 495-496?

@Cadix
Sorry, non of your images work for me (at least at the moment)

No, I actually completely forgot about this one, but it's a good one. The one I meant was on some homepage, but like I said, I can't remember where.

jeko wrote:@Cadix Sorry, non of your images work for me (at least at the moment)

@jeko I fixed the images, sorry about that

HankSimon wrote: I'm misquoting, but the gist is that Robert Lang related that Akira Yoshizawa had said that it took him 25 years to be happy with the design of an origami Swan (?) ... And, that Lang himself had become aware that he continued to re-visit one of his designs over a couple of decades ...

It was the Cicada.

I think you are in a mathematician universe you could produce origami in more than 3D.
I think this is the future of origami, do it in more than 3 D, but to do that it will be hard because it will be only possible with math and the result could be only a lot of algorithm without artistic value, but big value for the cience.

In future humankind could develop an origami on more than 3 dimensions. But first we need to undestand in 3 to make rules to extend them in n-dimesion.

These rules are not ready but i think we are close.

This is math-origami.

^Topologically speaking, aren't all origami models 2-D since we are folding the plane? Not that I doubt the existence of beautiful 4D forms generated by topologically 3D foldings of 3-space.

Speaking of folding in the realm of mathematics, their is a concept of turning a sphere inside out using a material that can be flexed and pushed through itself without the need to cut a hole, though creasing isn't allowed either. If we started with a plane of such material, removed the no creasing rule, I wonder what self-intersecting models could be created.

Stumbled upon the picture of the infinite Birdbases that I wanted to show earlier:
http://web.archive.org/web/201202180511 ... rd_bases_7

It's a theoretical construct of this simpler version that the author actually folded:
http://web.archive.org/web/201202180511 ... bird_bases