Origami Tessellations

I’m still folding paper - see some of the work at the end of this post! But I’ve just started taking GMAW/MiG welding classes, and it’s a lot of fun. I’m looking forward to learning some metalworking skills and applying some of my love for geometric design… and seeing what comes out of the combination!

I have a lot of fond memories of my grandfather working in his shop welding things, and my first attempts at welding tonight (while messy) made me feel a connection with him, and it was a happy-making experience.

And then this - my first exposure to a computer-controlled plasma cutter! It was love at first sight!

I have, however, been doing work in paper as well. I took a week in early February and went on a personal “art retreat” in NYC, and I was able to get some interesting work done. I also came away with a lot of ideas for new work, which is still continuing.

Here’s a design for a bowl (of all things) which I am still refining, to be completed in some wonderful multi-hued blue handmade flax paper. Please forgive the quality of the photos here, I was taking photos during the build process for my own reference.

Here’s the blue flax that I’m intending to use, from Cave Paper in Minneapolis.

And here’s a sample of a variant pattern folded from the same paper in a chocolate / brown hue:

The paper has a delightful roughness to it, with an uneven deckled edge that should really make a great rim to the bowl. I’m looking forward to the final version of this; I just have to make sure that I calculate everything properly, as I only get one chance to make it, and it’s going to take three sheets of the blue flax to do it in the proper scale.

If anyone has a good suggestion for a clear and strong glue, please let me know. I haven’t found any satisfactory “connecting” materials yet, which is also holding things up a bit. Ideas welcome.

Arms of Shiva, flagstone version (crease pattern)

Originally uploaded by EricGjerde.

This is a crease pattern of one of my designs[1][2] (which for the sake of convenience I have dubbed ‘Arms of Shiva’.)

However, this takes that design and throws it through the flagstonization machine, waterbombing all the folds to make the pattern you see above. While it might look like it is very wasteful of space (it is) there’s still less wasted paper doing it via this method than our normal straight pleat-and-twist methodology. Go figure!

I would love to see this folded, in case there’s anyone out there feeling intrepid enough to give it a try…

Pecten Magellanicus, Redux

Originally uploaded by EricGjerde.

A while back I folded a three-dimensional shell shape from some pleats, which I called “Pecten Magellanicus” (Sea Scallop), mostly due to the fact that it really looked like one.

I really liked the initial piece I did, and I wanted to see it realized on a larger scale. There’s a lot of pleating involved, so I decided to start off by folding four of them together, and then see where I wanted to take it from that point.

Here’s the initial version:

Pecten magellanicus, work sketch

However, in creating the second version, I didn’t properly sort out the ratios for the pleats. On the initial sketch, the rectangles that are used to create the pleat fan have a ratio of 2:9, for width:length. This made the shell shape fold almost flat when made with 7 pleats. On the larger version, I made a miscalculation and it ended up closer to a ratio of 1:5, which means the pleat fan extends farther upwards and is not as close to the flat plane of the paper on the ends. Thus the difference in the sides on this piece compared to the initial work sketch. Oops.

Anyway, this piece really isn’t close to finished, there’s a lot more that needs to be done with it. I’m not really happy with the ends of the pleat fans, so something needs to change there. There’s also a lot of extra paper and pleats in the middle that should probably have something interesting come out of it- no reason to leave good pleat space empty. Also, the whole thing hasn’t been wetfolded at all yet, so nothing is locked into place or flattened yet- thusly the bulbous appearance. Once it’s finished it should properly lay flat.

Just thought I’d share this with you since it’s going back into the “unfinished” box until after the New Year. Too much work to do right now to play with this any more, and give it the time it deserves to come out right.

-Eric

Continuing with the ideas of using negative space to form shapes, I tried to fold a traditional 5-pointed star. This required figuring out a few things, and to make life significantly easier for me I created a pretty simple crease pattern to use. However, a lot of the fold relationships with pentagons aren’t as easy to work out, and things don’t fold out to be easy distances like 1:2; with pentagons, they are primarily 1:1.6…, or 1/phi. I love the number Phi, and it’s really a fantastic thing, but folding it isn’t as easy! I’m sharing this example just to show it’s certainly possible, and hopefully to spur some other people on to see what they can do with the same sorts of ideas.

Here’s some photos of what I was working on; the backlit image has one corner which is folded differently, to illustrate the same kind of concept I used on my 6 sided stars. figuring out where to put all the creases was pretty tricky, although if I was doing it again it would be simpler. It’s definitely all about reference creases and lines.

And here’s the crease pattern I was using- it’s really more of a reference line sheet, than anything else. But it’s available to download if you’re interested.

Mosque Tiling with negative space, WIPOriginally uploaded by Ori-gomi.

The rendered product. hard to see with this paper, but it is a pattern of hexagon shapes in a hexagonal grid, connected by large stars with smaller stars set into them.

There’s a lot more that could be packed into this pattern, or changes made to the general folding of it- it’s quite flexible. the 90/120/90/60 intersections (the tips of the interior stars) are quite easy to fold, and that particular pleat/crease intersection can be made into dozens (literally!) of different things. It was hard for me to decide on this particular tiling and folding sequence.

Anyway, let me know what you think. I’ll use some unryu next time around.

Mask tessellation

Originally uploaded by Owesen.

Taking mask tessellations in the other direction, here’s a recent work in progress from Fredrik Owesen.

Masks made of tessellations, Tessellations made out of masks- anyone else have something to contribute?

This tiling is really just causing me mental anguish. I’m trying to find an elegant way to fold it, and it’s just not happening so far.

(click the photo for a larger version)

Totally open to suggestions or hints from crowd on this one. it’s really interesting looking, too… what I have folded so far is fascinating (to me, anyway). I’d really like to find a way to make it go the distance.

WIP triangle fold, redux (reverse)

Originally uploaded by Ori-gomi.

a slightly different attack on the triangle thing. can you tell that when I mentally envision something, I have to create it or it drives me nuts? this design is giving me stress, and I want to complete it and be done with it already.

regardless, here is a modified base, folded from a sheet of treated unryu. it’s actually one of the scrap pieces left over from my testing process, which explains the random edges, etc.

it’s very lovely paper, and is great to fold- it’s extremely thin, but treating it properly makes it stiff and springy. much more so than standard kami (the paper you buy in a pack of 100 from the paper store.)

Something else worth noting here- on the star version of this fold, you’re taking a pattern with hexagonal symmetry which gives you 6 shapes (thusly, 6 triangles). if you try the same methodology with triangular symmetry, you get 3 shapes with 6 sides. I suppose this is rather obvious, but it’s still interesting to see it play out this way.

on the larger version of this that I did (here), I ended up with some odd hexagonal shapes on the bottom that became larger and larger as my folds progressed.

I need to refold this newer variant on larger paper that is more forgiving, so I can do better manipulation of my crease points and all the complicated sinks.

unnamed design in process, WIP, backlit

Originally uploaded by Ori-gomi.

Fooling around with some of the same folding concepts behind the star twist v2.1. interestingly enough, doing the same process with a triangle base yields odd hexagonal shapes as one grows increasingly larger.

However, so far they are overly clumsy, and multiple attempts have not found a more desirable folding method. too much extra paper on the reverse so far. time to unfold and try a different attack.

Folded the original design out of unryu, which was much more compliant for such a layered concept- this sheet of standard kami is giving up the ghost.

look for a future photoset detailing a simple method of producing wonderful tessellation paper, soon!

I received a great email from Danilo in Chile, with a bunch of great photos attached- I’d like to post them but I’m waiting for his permission first. His origami group in Chile has a website, located at www.origamichile.cl. It’s very nicely laid out and has a bunch of stellar photos and diagrams. Someone definitely went through a lot of work to put that site together!

Since there seem to be a bunch of people visiting from Brasil and Chile, I’m going to hit up my nice Brasilian coworker to translate some of my documents and web junk into spanish (and Brasilian Portuguese!) for me. Hopefully he can make it a little better than Babelfish does!

I’m plugging away at some new materials, worked a bit on some existing crease patterns for release but I spent quite a few hours today trying to fold arbitrary angles to see what it takes to solve that problem. and the answer is… lots of math! it hurts my head! something that Alex Bateman should be programming, instead of me trying to figure out with a ruler and folding… I did come up with a pretty freaky pattern (to me) which I will scan and post tomorrow. it actually goes a bit of the way towards solving some complex tessellations of the euclidean plane, which really surprised me a bit. Kind of neat, although I got strung up by not knowing where all the “next folds” should go.

Anyway, that’s for tomorrow!