Test Folds: Assorted Corrugations

The full box of corrugations

The full box of corrugations

Over the past month, I have been test-folding lots of corrugation patterns in preparation for a new series. Most of these are not original designs; they are folded from crease patterns, reverse-engineered, or experiments vaguely based on images from the Flickr Origami Corrugations group. These are all folded from very cheap origami paper, not anything at all suitable for complex designs. I have previously folded a couple designs incorporating both pleated and corrugated segments, but only with very simple corrugated patterns. I am hoping that with more practice, I will be able to incorporate more complex corrugations and tessellations into my vases.

Here are a couple closer-up images of some of the corrugations:

Close-up of a few corrugations

Close-up of a few corrugations

Close-up of a few corrugations

Close-up of a few corrugations

Close-up of a few corrugations

Close-up of a few corrugations

New Work: Double Diagonal Shift Vase 3

Double Diagonal Shift Vase 3

Double Diagonal Shift Vase 3

This piece is part of my Diagonal Shift series and is very strongly based on one of the earliest pieces in the series. I used (almost) the same crease pattern but re-designed the painted pattern. The painted pattern is somewhat reminiscent of my Floating Diagonal Shift, where the painted parts would align if the segments of the vase were aligned with each other. I enjoy creating the illusion of impossibility with these pieces.

New Work: Diagonal Shift Variant Vase 2

Diagonal shift variant vase 2

Diagonal shift variant vase 2

This piece is a continuation of my Diagonal Shift series, building especially from one of the earlier pieces in the series. When I first tried folding this concept, there wasn’t enough difference between the slopes of the diagonal line and the horizontal line, so the two halves of the vase weren’t clearly separated enough. When I re-designed the form for this piece, I made the diagonal much more dramatic. This creates an illusion that the top half of the vase is balancing on the tip of the bottom half. Of course, as in the other pieces in this series, there is a narrower piece connecting the two halves.

I also played a bit more with the colors in this piece. The copper and the green-gold give more color contrast than I have been using. Also, it’s not obvious from the photo, but the copper areas have a thin layer of copper paint over a layer of gold. The subtle color differences add more interest to the piece.

New Work: Rotated Diagonal Shift Vase

Rotated Diagonal Shift Vase

Rotated Diagonal Shift Vase

I’ve folded quite a few pieces in my Diagonal Shift series recently, and this piece is the latest addition to the series. In all of my previous pieces in the series, I’ve either used only one diagonal shift element or used two diagonal shifts in the same plane. In this piece, the two diagonal shifts are rotated 90 degrees from each other, and the painted designs follow the same pattern rotation. Keeping track of the rotation made this piece especially challenging to design, particularly drawing the crease pattern onto the paper.

It’s interesting to see how this piece came out. Since most of the pieces in this series have all their angles in the same plane, there are a few very interesting viewing angles, but the other views don’t add much of anything. But this piece has a more complicated geometry in three dimensions. It’s hard to pick a view to photograph because there isn’t any one angle that shows the full shape (more views below). Seeing the relationships between the shapes from a variety of angles make the piece more interesting to look at in real life.

Rotated Diagonal Shift Vase (view 2)

Rotated Diagonal Shift Vase (view 2)

Rotated Diagonal Shift Vase (view 3)

Rotated Diagonal Shift Vase (view 3)

Rotated Diagonal Shift Vase (view 4)

Rotated Diagonal Shift Vase (view 4)

Test Folds: Assorted Tessellations

I recently returned from a long plane trip, and I had a lot of time for origami while in transit. Since my typical folding style isn’t very conducive to folding while traveling, I decided to practice folding tessellations from Eric Gjerde’s book, Origami Tessellations: Awe-Inspiring Geometric Design. It’s a nice introduction, building up from the basic folding techniques to a variety of simple and complex tessellations.

Tessellations

Tessellations

I have folded a couple tessellations before, but this was my first time folding a lot in a short period of time. I learned the proper way to fold grids to minimize errors, but folding the grids still takes a long time (for 32 divisions, close to an hour for a square grid and longer for a hexagonal grid). These tessellations are all folded from cheap 6-inch squares of paper, which isn’t ideal. The paper gets soft too quickly, which limits the complexity of the models I could successfully fold. I would like to eventually incorporate more tessellated/corrugated elements into some of my own 3D designs, but it may still be a while before I build up the skills to do that well.

Tessellations 1

Tessellations 1

Tessellations 2

Tessellations 2

Tessellations 3

Tessellations 3

Tessellations 4

Tessellations 4

Tessellations 5

Tessellations 5

 

Crease patterns: Diagonal shift variants

I’ve previously posted several crease patterns for my diagonal shift designs. Since posting those crease patterns, I designed a diagonal shift variant where the top and bottom halves of the paper form tubes of different widths and folded several models based on that design. Here are some crease patterns for a couple versions of diagonal shift variants. The dimensions on these don’t quite match any of the models I’ve folded, but they at least show the approach I used.

First, the single diagonal shift variant:

Diagonal shift variant

Diagonal shift variant

The bottom half of this crease pattern is identical to the crease patterns I posted before. Just above the middle, the diagonal lines only go partway past the middle of each gore, and the top section forms a narrower tube. This crease pattern gives something similar to the central part of this model.

These designs can also be combined in a couple ways. One option is to mirror the diagonal shift element vertically, giving a double diagonal shift pattern like the one in this vase:

Double diagonal shift variant

Double diagonal shift variant

Another other option is to also shift the top diagonal shift section over by 8 gores (half the width of the paper, excluding the overlap), which gives something like this model:

Double diagonal shift variant 2

Double diagonal shift variant 2

The math behind these designs is a good bit more complicated than I enjoy doing by hand, so I’ve set up spreadsheets to automatically do most of the math for me. I haven’t written about that aspect yet, but I might do that at some point when I have time.

Two upcoming shows!

I’m very excited to announce that I’ll be participating in two origami shows this summer!

1. FAVA Folding Festival

The FAVA gallery in Oberlin, OH has been hosting the FAVA Folding Festival since 2008, organized by James Peake. The info for this year’s show isn’t online yet, but the show will be open from May 11 until late July. I will have about 6 pieces in the show, including selections from both my Intersections and Diagonal Shift series.

2. Surface to Structure

Surface to Structure: Folded Forms will be exhibited at the Cooper Union in New York City. This was also the site of the first origami exhibit in the United States, in 1959. The show will be open June 19 – July 4 and is curated by Uyen Nguyen with co-advisors Sok Song and Patsy Wang Iverson. I will have one piece from my Diagonal Shift series in the show.

Test models: Diagonal Intersections

Bisected diagonal shift

Bisected diagonal shift

This test model is a combination of my two recent series: Diagonal Shifts and Intersections. Even though this piece worked decently as a test model, it doesn’t work quite well enough yet for me to use this in a real model. Hopefully if I do another test fold, I’ll be able to fix some of those problems.

I’ve done a lot of engineering to figure out how to fold my recent series, but I haven’t shown much of the process. This time I took some photos of my first couple test folds to share. I started with some of the measurements I’ve previously used for the diagonal shift models. Creating the flat plane of the model is basically just folding down a rhombus to a single line. My first attempt was to fold the central rhombus into a waterbomb base:

Diagonal intersection draft 1 back

Diagonal intersection draft 1 back

Diagonal intersection draft 1 front

Diagonal intersection draft 1 front

This design looks great from the front, but the back won’t work for the full model. The large triangle sticking up in the back will get in the way of the curved portion of the model. A good start, but not quite useable.

Then I started trying to figure out how to get rid of that extra triangle. I started by inverting the waterbomb base so the triangle was sticking out the front of the model instead of out the back. Then I squash-folded the triangle to flatten it against the front of the model:

Diagonal intersection draft 2 back

Diagonal intersection draft 2 back

Diagonal intersection draft 2 front

Diagonal intersection draft 2 front

This design is much better from the back – there’s no extra paper between the two flaps along the central diagonal. That means I should be able to use it for more complex models. The problem is that the front is very messy-looking: the extra paper from the central rhombus is visible and not especially nice to see there.

In my third test fold, I combined the best parts of my two first test folds. I squash-folded the central rhombus, but I also hid the extra paper on the back side of the model:

Diagonal intersection draft 3 back

Diagonal intersection draft 3 back

Diagonal intersection draft 3 front

Diagonal intersection draft 3 front

This final design is what I used in the full test model (photo at the beginning of this post). I combined it with the diagonal shift approach I’ve already written about. Combining the flat part and the curved part is still a challenge, but it’s one I’m working on. I’m hoping to fold at least one or two full models based on this design, but it may be too complicated to turn into a full series.

Test model: Organic bowl

Organic bowl

Organic bowl

It’s probably fairly obvious that this model is a departure from my normal folding style. Almost all of the folding I’ve done recently has been highly mathematically, precise, and planned. I have folded more organic pieces before, but it’s been a long time. Even those pieces were fairly structured and mathematically based.

This is probably first piece I’ve ever folded without making any actual measurements, and it was completely an experiment. I started by tearing a vaguely round-ish piece of paper from a large scrap I had sitting around. I used a compass to estimate some sizes and divisions and a ruler as a straightedge, but the rest was all free-folded. The flat base is in the center of the paper. I knew there would be a lot of extra paper around the edges, but I didn’t know¬†what the outer sections would look like until I was mostly done folding. I did several rounds of wet-folding and taping the paper into various shapes until I got the paper into a shape I liked.

Organic bowl

Organic bowl (view 2)

I had a lot of fun folding something completely free-form, and hopefully I’ll try it again sometime. I’ve been wanting to do some more organic designs for a while. Eventually I’d like to develop a folding approach somewhere between the purely mathematical and the purely free-form, but that’s something I’m still figuring out how to approach.

Organic bowl

Organic bowl (view 3)

New work: Diagonal shift with a size change

Diagonal shift with a size change

Diagonal shift with a size change

This piece is a return to my diagonal shift series, which I took a short break from. I used the same diagonal shift variant element as in my most recent two pieces in the series. This time, instead of using two diagonal shifts to transition from a wide cylinder to a narrow one and then back to a wide one, I only used one diagonal shift. The sizes are aligned so the outer edge on one side is an unbroken curve.

One of the challenges I often run into in designing models is figuring out how my sketch will actually look in three dimensions. Since I have to figure out all the dimensions of the model before I do any folding, it’s very important that my sketch has the proportions I want. But in this piece, the change from a 2D sketch to a 3D folded model changed how the proportions look more than I expected. In the sketch, the top and bottom halves looked more evenly balanced; in the model, the bottom half has a good bit more volume and more visual weight. Even if this piece didn’t look quite like I expected, that makes it more of a learning experience for me than folding something that works exactly how I expected.