Origami Tessellations

Ron Resch, curved folds (from Ron Resch)

I highly recommend you check out the fledgling website belonging to Ron Resch, a visionary mathematician and designer who was one of (if not *the*) first to explore the architectural potential of 3D tessellated structures in the 1960’s and 70’s.

Only lately have I been exposed to more of his work, and the more I see the more I want to know. He has a film- called “The Paper and Stick Film”- which is apparently quite a fascinating thing to watch. He has a link to purchase this from his website, but it still seems to be a non-functioning link. (The minute this becomes available I’m buying it!)

It looks like he updated his site with some more photos of his patents and some additional historical photos of things he has worked on, too, so if you’ve been to the site before I suggest visiting it again.

Tom Hull talked a good bit about Resch at the Origami USA convention this year, and really intrigued me to look further into his designs. Only recently have I started exploring 3D tessellations myself, and so seeing his innovative thoughts from way back when is really an eye-opener for me.

One thing that really hit me today as I was looking at his site (yet again) was this curving folded piece, made up of out pleats. I like the way it captures an essence- flight, perhaps, or maybe something a bit more ethereal than that.

Sometime soon I need to make a pilgrimage up to Vegreville in Alberta, Canada to see his giant Easter Egg, made for the large Ukrainian community on the High Prairies to celebrate their heritage. There’s some more information about that on his site as well, which is worth looking at. Do a google search for it too, you won’t regret it.

-Eric

Update 2012: As Ron Resch has passed away, his website has fallen into the hands of domain scavengers – so I’ve removed the links to the content. If it reappears somewhere else in the future I will re-link.

Pecten magellanicus, work sketch

Originally uploaded by EricGjerde.

I’ve been spending way too much time lately exploring pleated, three-dimensional structures.

With this little fold, I was wanting to see a 3D shell-like fan shaped piece; it’s not really quite what I was looking for, but it’s also interesting, so I left it as-is with the intention of trying to make another one later. After wetfolding it a bit (to assist with the thick pleats at the center) the shape kind of grew on me.

I recently folded a much larger sheet of 4 of these shapes- essentially a tessellation of this design. It is nice, but I wasn’t quite happy with how it turned out- there’s a really complicated bit of magic involved with how the pleats + diagonal creases work out, so even if your rectangles are off by a tiny bit you don’t get the same result. In this design, the ratio of the rectangles is 2:9, for reference, which seems to work the best; the larger example I made is more like 2:9.5, and that doesn’t come out the same.

I’ll post some photos of the larger version when I eventually get around to wetfolding it all, but that might take a bit of time. There’s also the matter of excess paper that needs some ornamentation but I have yet to decide what to do with it, so until a solution presents itself it is living in the “unfinished” box… which is getting rather full, these days.

I called this design “Pecten Magellanicus”, named after the sea scallop, which it reminds me of. Since the fold itself is thick and 3D, it has a very strong resemblance to this little shellfish, even if the geometry is a little off.

Yuko Nishimura Ripoff

Originally uploaded by Owesen.

Fredrik Owesen did some reverse-engineering of the folding techniques mastered by Yuko Nishimura, a long-time favorite of mine. (if you like pleating and tessellations, Nishimura is probably also a favorite of yours, too!)

Fredrik gave a little description of how to accomplish this type of folding:

I’ll try to write up some sort of how-to, although I suspect they tend to be confusing.

I’ve grown pretty lazy in terms of folding methods lately, so this will be based on that. You begin by drawing the crease pattern on the sheet you want to fold, using a sharpish ballpointpen, one without ink or a color matched to the paper is good. First lines divide the sheet in long rectangular lines (1). Turn the sheet, then using some sort of curved guide (found a cheap flexible ruler well suited for the purpose), fill in the curves that go between the lines from the previous step.

Use the lines you just drew, both curved and straight, to mark up a grid by forming lines perpendicular to these. The curved lines will give the grid some unevenness, but when forming the grid treat them as straight lines, ignoring the spacing. Turn the sheet over and create a similar grid 50% ofset from the other.

Using these marks it is easy to fill in the zigzag pattern, mountainfold on one side, then flip the sheet over for the valley folds. Collapse it into shape when all the creases are there.

I’ve long wanted to fold something like this, so thanks for the hints, Fredrik. Now to sit down and give it a try…

Circus Circus

Originally uploaded by lilzabubba.

I’m fascinated by the complex geometric patterns involved in this traditional Japanese embroidery craft. It’s all types of tessellations of the sphere, which is utterly different than the flat plane tessellations I work on- so things like pentagons are able to tile without difficulty. I must admit I’m a little envious of how nicely things tile on the surface of a sphere. I think perhaps we are missing some of the intriguing geometric connections that the world is offering us!

I’m a big fan of flickr Temari crafter lilzabubba, who seems to make a new one of these every other day. A good mental break from the tyranny of the two dimensional plane of existence.

Propellerheads

Originally uploaded by EricGjerde.

We’ve been talking a lot in the Origami Tessellations group on Flickr about “flagstone” tessellations, so named by Joel Cooper for their distinctive look. They are a favorite of his, and since his work is where we were introduced to the concept, the name seems quite appropriate.

There’s a lot of weird folding voodoo that goes on with these folds, which we’ve all been trying to figure out and explain; some of us much better than others- Peter, Lorenzo, and Jorge having more luck here due to their mathematical orientation.

I’ve noticed a strange correlation between iso-area folds and the “flagstone” process, and in trying to understand it I started folding a simple, offset iso-area square twist (seen in the picture above). However, since I’m folding with elephant hide, it has a very nice sculptural quality to it, and makes some very nice curved shapes. So I “froze” the squashing process half way, making these rather interesting 3d puffs. I like the way it introduces a curving element to the angled pleats, and really does resemble a tiling of airplane propellers. This probably deserves to be given a larger treatment at another point in time.

The reverse side looks like this: