After another long trip, here are some more tessellations. There’s an assortment here of designs folded from instructions, designs reverse-engineered from pictures of the folded models, and my own designs (which may be re-inventions of other people’s models).
… I do something like this:
I like folding tessellations while traveling because they are easy to transport (small and mostly flat) and relatively repetitive to fold because of the repetition in the grid and symmetry of the pattern (and so possible to do when I’m tired). All of these are folded from squares of Elephant Hide paper, some painted with acrylic paint. This paper is great for tessellations because it holds up through a lot of folding and unfolding without getting mushy, which many of the more complicated tessellations require.These models are all folded directly from or adapted from Eric Gjerde’s book Origami Tessellations.
Here are some close-up images of some of the tessellations:
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:
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.
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.
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:
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:
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:
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.
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.
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.
I recently folded an initial test model with a diagonal shift. At that point, there were still quite a few problems with my test model, including a combination of mathematical complications and folding difficulties. Since then, I have made several changes that help solve those problems without significantly changing the appearance of the final models:
To make the math easier, I created an Excel spreadsheet that automates most of the calculations based on the distances and angles between each fold. This is the first of my models where I have relied on the computer to help figure out the dimensions. I also made a change to the crease pattern that simplified both the folding process and the math.
In my new folding process, the diagonal shift creates a half-twist in the paper, so the paper on the far left above the diagonal shift ends up on the far right on the bottom half of the model. The amount the top and bottom halves are shifted along the diagonal is related to how steep the diagonal is. When the diagonal is close to horizontal, there is very little shift. As the diagonal gets steeper, the amount of shift increases.
I am planning on incorporating this design element into more complex models and hopefully posting some crease patterns soon.
Why should circles get all the attention?
I’ve experimented a bit with breaking away from circle-based designs previously in models like my seed pod bowl and spiral bowl, but this design is the furthest I’ve deviated from a circle. The oval is made of portions of two sizes of circles, one with a radius of 1 inch and the other with a radius of 4 inches. The two ends are each 3/8 of a circle (135 degrees) with the small radius, and the two flatter sides are each 1/8 of a circle (45 degrees). That means that the four segments add up to 360 degrees, one full rotation.
The flat base on this shape (shown in the image above) doesn’t close nearly as nicely as most of the circular designs I fold. To get the base to stay flat, I had to wet-fold it and weigh it down while it dried. My circular bases usually stay put without any wet-folding. Even though the edges of the paper line up correctly, it’s easy to open a wide gap. Without adding glue, anything I put inside this model would probably just fall through the bottom.
Despite the extra challenges, I think this approach is ready to use on more complicated models. The model fits together exactly how I expected it to based on the math, and the folding process is certainly doable.
This concept is an extension of the ideas I worked on this winter and early spring, particularly my Intersections series and my last test fold. Like those earlier pieces, I’m combining a curved form with a flat plane. The difference here is that instead of the flat plane being perfectly vertical, here the flat plane is along a diagonal. This requires a very different folding strategy.
I have several ideas of where I’d like to go with this folding strategy, but for now I’m still working out the engineering for it. This test piece was folded from a fairly simple-looking crease pattern, but actually folding it was surprisingly difficult. Even using Elephant Hide paper, which is a very tough paper, some of the internal layers started to tear. I want to try various tweaks to the proportions to see if I can find a version that collapses more easily. Also, in my current version the flat plane is essentially a circle, but it should be elongated into an ellipse. If I can find a way to cleanly fold an ellipse, that may remove some of the distortions to the tube.
This model is a practice piece, somewhat building on my Intersections series. It’s the first model with no curves that I’ve folded in quite a while. Since the top diagonal plane is intersecting a simple square box, it’s not too hard to figure out how to tuck the extra paper inside. However, that will change very quickly if I move to more complex shapes. I like the simplicity and sleekness of this form, which gives a very different aesthetic than my normal folding style. This piece is folded from one uncut rectangle of Elephant Hide paper.
