I’m pleased to announce that my series of three curved-neck vases is now part of the permanent collection of the Museo del Origami in Colonia, Uruguay! The museum has a few more details on the addition on its news page.
The Museo del Origami opened in 2020 and is the only museum in the Americas that focuses exclusively on origami. Their permanent collection traces the historical development of origami in both the East and the West, highlights the work of contemporary origami artists across many design styles, and explores applications of origami in science, technology, education, and design.
I realized recently that it’s been just over ten years since I started designing origami vases and bowls! That’s a good opportunity to show off a few highlights of how my artwork has grown and changed over that time.
The pre-design days
Even though I’ve only been designing for ten years, I’ve enjoyed doing origami since preschool. In college, I got really into modular origami, and quite a few of my friends ended up with gifts of various models. As a double-major in art and chemistry, origami-related themes were a recurring theme in my artwork. My senior art show in 2009 at Furman University was a series of 24″ x 24″ oil paintings of paper cranes.
Gold crane (2009, oil on canvas)
The first designs
After I started grad school in chemistry, I no longer had the large blocks of times I needed for painting, but I still have a drive to create. In spring 2011, I went to a lecture by Robert Lang where he talked about the math and engineering in origami, which inspired me to get back into origami. I had a very brief foray into folding representational models, but quickly figured out I wasn’t actually all that interested folding those. While looking for crease patterns online, I stumbled upon Philip Chapman-Bell’s Flickr page, where he had several crease patterns of curved-crease vases. I folded a few of his crease patterns and realized the math behind them couldn’t be all that complicated. My first design was a little underwhelming, but it was enough to get me hooked.
My first curved-crease vase (May 2011)
Curves and organic shapes (2011-present)
It only took me a few months to get bored with only folding designs based on symmetric curved-crease pleats and start exploring ways of distorting the symmetry. One of my earlier explorations was spirals, which worked out best in the piece I’ve used as a profile picture in quite a few places in 2012.
Spiral bowl (2012)
I’ve never done an extensive series of more organic forms, but I’ve had quite a few brief forays into designs that are based more on curves. The curved-neck vases are one of my favorite examples of that. The design elements used to create the curved necks are the same ones I’ve used in a number of more geometric-looking vases, but applied in a slightly different way.
Curved-neck vases 1, 2, and 3
Intersections series (2012-2014)
The first major series I did was based on taking curved-crease pleated vase/bowl forms and intersecting them with vertical planes. There were two main things that attracted me to creating these types of designs. The first was the engineering challenge: figuring out how to combine the curved forms with flat planes. The second, more aesthetic goal was also a big piece: combining geometric elements that represent my scientific interests with more organic elements that represent my artistic interests.
Split vase
Diagonal shifts (2013-2014)
The series that started getting me a good bit of attention in the origami world was my diagonal shift series, where the curved form is cut by a diagonal plane and shifted. I love how the diagonal shift element leads to shapes that look like they should be impossible to create from a single uncut sheet of paper, even though the shift along the diagonal comes very naturally from the construction of the twist. I also like how these pieces initially draw people in based on their aesthetic qualities, but once I have them drawn in, even people from outside of origami switch over to trying to figure out how they work. I have the privilege of using art to bring out people’s scientific/engineering thought processes! I realized after I started this series that part of the inspiration probably came from my visit to the Magritte museum in Brussels and spending a day there looking at his Surrealist artwork.
Floating diagonal shift vase
More exploration of distorted vases (2016-present)
A couple years after the original diagonal shift series, I started extending the geometric distortions to more complicated versions. These pieces are very modular, based on stacking different twist and bend motifs in various ways. I’m still working on developing more motifs that let me distort the vase-like forms in new ways, and on combining them to create interesting forms.
Doubly bent vase
Mixed media (ceramics 2015-2016, knit 2020-present)
One other interest I’ve had is combining other media with origami. My first foray into that was with ceramics. Since working on the pottery wheel naturally tends to produce shapes that are similar to the pleated vase forms, it seemed like a good fit. I enjoyed finding ways of getting the clay and the paper forms to mimic each other.
Origami/ceramic wavy vessel
More recently, I’ve done several pieces combining knit forms with origami. It’s taken a decent bit of work to figure out how to construct shapes similar to my origami forms in yarn, and that’s something I’m definitely still figuring out. Stiffening the yarn is a very slow process that I haven’t figured out how to speed up, so I’m still deciding whether this is a direction I’ll take much further.
I’ve played with folding tessellations on and off for quite while, but never had a lot of success combining them into my bowls and vases (my last attempt from 2015 has been lovingly nicknamed the Easter grenade). This bowl is a new and more successful attempt along those lines.
Diamond-edged vase
The bowl is folded from a circle of Elephant Hide paper, and the tessellation grid for the diamonds is a modified triangle grid follows that curved edge. The radial lines were fairly straightforward to set up, except that it’s a bit tedious to divide the edge of a circle into 160 equal segments. The other sets of lines are slightly curved so that all the triangles are close enough to equilateral to collapse correctly in the folded model. The grid is only on the outer rim of the paper, which lets the lower part of the bowl curve smoothly. The tessellation itself is fairly simple – basically pairs of rhombus twists that are aligned to look like a row of vertical diamonds.
I’ve played quite a bit with ways to curve the axis of paper tubes, starting with simple pleats and extending to the crimp-bends that I used in my curved-neck vases and an assortment of geometrically distorted models. The crimp-bends have some advantages, but are a lot of work to set up for tubes with vertical pleats.
These test folds are a return to simpler pleats, testing how easily I can fold a series of pleats along the length of a tube. The first one is a test of changing the pleat axis along the length of the model, creating a slight helical twist.
Helical pleated tubeHelical pleated tube
The second keeps the same axis but changes in width along the length of the tube.
This vase is part of my series of geometrically distorted vases, incorporating a tilt of the main axis of the vase. This vase is similar to one of my recent models, and since that model I’ve figured out how to adapt the curved portions of the vase to keep the horizontal planes all closer to exactly horizontal. The shift in the middle uses the same pattern as my downhill diagonal shifts, with the angle chosen to match the tilt of the vase.
This model builds on my recent offset bowl, where the model is based on a tilted cylinder. Here, I added curved folds and painted lines to the tilted cylinder, fitting it into my geometrically distorted vase series. The central bend is similar to my previous designs, and the top and bottom planes are also defined by sine waves to transition between the tilted cylinder and flat planes.
In my last tutorial, I gave step-by-step instructions on how to fold a vase using a pleated folding technique. In this tutorial, I’ll talk about how to design your own pleated vases and bowls. This post will focus on how pleated folding works, and later I’ll write a tutorial on how to calculate the correct dimensions for any shape. To start, here’s the pleated vase from my last tutorial:
Pleated vase
Why does this crease pattern fold into that shape? Let’s start from very simple crease patterns and work our way up. Imagine that you took a long piece of paper and accordion-folded it, using equally spaced mountain and valley folds. All of the layers of paper end up on exactly top of each other to make a very narrow strip of paper.
Accordion folded strip of paper
Now imagine that instead of the folds being equally spaced, the pattern goes something like this: large gap, mountain fold, small gap, valley fold, repeat. If this pattern is folded, the layers won’t end up exactly on top of each other. The paper will be somewhere between the length it was when the folds were equally spaced and the length of the original strip of paper. As the small gap gets smaller and the large gap gets larger, the folded strip of paper gets longer.
Accordion folded examples with unevenly spaced folds
Now let’s take those three examples and attach one end of the paper to the other end to make a tube. In all three examples, the paper starts off the same length. In the first example where the folds were equally spaced, the paper forms a very narrow tube. The more unequally spaced the folds are, the wider the tube is.
Accordion folded tubes
From these simple examples, we can understand how the pleated forms work. Just like the accordion-folded examples, the crease pattern below is based on alternating mountain folds and valley folds. In this example, the valley folds are straight and the mountain folds are curved. Either the mountain folds or the valley folds need to be straight lines; otherwise the form doesn’t collapse cleanly. We can think of the shape as a tube like our last set of examples, but in this case the width of the tube changes.
Crease pattern for pleated vase – click to enlarge
At the bottom edge of the crease pattern, the mountain and valley folds are equally spaced. Based on our accordion-folded example, that means the tube should be very narrow. And that’s what happens: at the center of the base, the layers of paper all match up, closing off the base. About a quarter of the way from the top edge, the mountain and valley folds in each pair are almost on top of each other. Here we expect the tube to be very wide. Again, that’s what happens: the place where the mountain and valley folds are closest together becomes the widest part of the vase. At the top edge of the crease pattern, the mountain and valley folds are somewhere in between – not evenly spaced, but not on top of each other. The top edge of the crease pattern becomes the rim of the vase, which is intermediate in width.
Pleated vase
Here’s one more example. In the crease pattern below, the folds are equally spaced at both the top and bottom edges, and there are two places in between where the mountain folds curve so far out that they touch the valley folds. So in this model, both the top and the bottom are very narrow and there are two widest points in between.
Crease pattern for ornament – click to enlarge
Ornament
Stay tuned for my next tutorial on how to figure out the dimensions for the crease pattern.
I have always been interested in both art and science. Growing up, I thought of those two interests as being more or less completely separate. As I progressed through my college studying both chemistry and studio art, I started seeing connections between the two. My artistic training helped me visualize molecules and reactions in 3D, and my art became very structured and organized, using the same sort of logical connections I used in my science classes.
After starting graduate school, I had my interest in origami rekindled. I discovered the geometric folding style to create curved, flowing vases and bowls that others had developed, and very quickly I was hooked. From looking at crease patterns posted online, I realized that I could figure out the math behind their designs and very quickly moved on to creating my own designs. I was drawn to both the aesthetic qualities of the origami and the mathematical challenge of figuring out how to create interesting shapes from just a piece of paper.
My design process is a melding of artistic and engineering approaches. I want to create shapes that are visually interesting and appealing to look at. At the same time, the design process is heavily driven by the engineering aspects of figuring out how to turn one uncut rectangle (or rarely, a circle or another shape) into a complex shape. The inspiration for specific designs comes from both aspects. Some designs are mostly driven by a shape or an idea I want to capture in paper, and others are based on something an engineering motif that I think could be used in interesting ways artistically. When I have a new idea, I often spend time working through the math and test-folding simple pieces until I have a folding strategy that works.
Once I have a folded motif engineered, incorporating it into a finished model or series is usually the more straightforward part. For each piece, I start with a sketch on graph paper, to scale. At this point, I know in general how the folds in the crease pattern will fit together. Then, I calculate the precise dimensions. Some of the calculations involve relatively straightforward geometry such as calculating the circumference of a circle, but others are complex enough that I have incorporated them into computer scripts.
I only start working on the piece after all the folds and dimensions are planned in full detail, to the nearest 0.5 mm. I work almost exclusively using Zanders Elephant Hide paper. I cut the paper into a rectangle of the correct size. The first step is painting the paper with watered-down acrylic paint. I measure all the necessary reference points and tape off the edges to get clean lines; since I know where all the folds will be, I align the paint with where the folds will later be. Then, I start folding. I re-measure the reference points on the reverse side of the paper and score all the folds with a sharp tool. For straight folds, I can simply score against the edge of a ruler; for the curved folds, I usually cut a template and score along the edge so that all the curves are identical around the form. Then, I pre-crease all the folds and start collapsing the piece. I use a little glue to turn the paper into a tube but try to minimize glue elsewhere in the piece. Some sections of the model hold together just from the folds, but many of the curves need to be wet-folded and held in place with tape until they dry. Even though some pieces are more driven by the aesthetics and some are more driven by the engineering, the design and folding process for every piece incorporates elements of both.
In my work, I have incorporated the idea of the intersection of art and science visually through the relationships between straight and curved lines. Through a series of folds, the flat rectangle of paper is transformed into a curved, flowing surface. But the transformation also goes the other way: folds and paint lines that are sinusoidal on the flat paper create flat planes in the folded forms. I have explored variations on this theme, changing angles and locations of the flat planes and the shape and color relationships between the divided parts.
I hope my work will give you a glimpse of how I see the world. I want you to see the simple beauty and elegance of the forms and also think about how the shapes are constructed from uncut rectangles of paper. When I see the world (whether a sunset or a tree or a building), I don’t just notice the colors and shapes, but I also think about how light is absorbed or scattered to create those visual effects and what sort of science and engineering is going on under the surface. I hope my work will inspire you, even just for a minute, to see the beauty of your surroundings and think about all the incredible inner workings behind it.
