Inspired by my diagonal shift pieces, this model is a test piece incorporating several diagonal planes. The base, central plane, and top edge are all defined by sine waves. Unlike my previous models, these sine waves create three planes parallel to the table but tilt the central axis of the bowl. This is fairly straightforward to do with all straight folds, and I’m exploring whether this concept can be used with curved folds in my more complex diagonal shift designs.
Crease pattern: Bend variation
I designed a variation to my crimp-bends last spring, and here is the crease pattern. The concept is similar, but instead of being based on two sine waves, this version is based on one sine wave and one straight horizontal line. In this variation, part of the flat plane joining the top and bottom tubes is exposed. So far I haven’t figured out a mathematically correct way to place the central line such that the joining plane folds flat, but it comes close enough to work in practice.
As usual, I designed an ornament this year, similar to my designs the past several years. The paper is hand-painted with several layers of watered-down acrylic paint, which gives a texture a lot like watercolors. It doesn’t show much in the photo, but there’s a thin layer of silver paint on top that gives it a hint of sparkle.
Crease pattern: Downhill diagonal shift
I posted a photo of a test model of the downhill diagonal shift earlier this year. Here is the crease pattern for that model. The central part of the crease pattern is exactly the same as the standard uphill diagonal shift I’ve posted crease patterns of before. The top and bottom sections are the crimp-bends I recently posted and build on the sine waves used in the central diagonal shift. Since each portion of the crease pattern is a distortion of a tube, it’s fairly straightforward to stack these in all sorts of interesting combinations.
Downhill diagonal shift
Wide and narrow crimp bends
I previously posted images of these crimp-bent tubes that I designed earlier this year, and here are the crease patterns. The top and bottom edge of each bend are based on sine waves. The angles of the internal crimps on each vertical gore use the same math as the diagonal shifts, where each diagonal fold is angled toward one convergence point.
Crease pattern: Narrow Crimp bend
Crease pattern: Narrow crimp bend
Square/circle twist vase
This vase builds on my recent exploration of twists in non-cylindrical tubes. The central twist in this model is a 16-sided twist in a square tube. Like in my previous test fold, the twist naturally creates segments of parabolas on each face of the square tube. I repeated the parabolic shape several times to create the wavy painted pattern with a color gradient.
I bought this marbled paper several months ago because the colors and shapes within the marbling reminded me of a peacock. This vase has a fairly simple shape, also inspired by a peacock. This is a softer paper than I’m used to folding, even after being treated with methylcellulose, but it works for forms of this level of complexity.
This piece builds on my helix from several months ago. The neck of the vase uses a series of crimp-bends at different angles. The crimp-bends are pretty labor-intensive to fold, but it creates an interesting effect. Here’s a second view to show the curvature of the neck more clearly:
Curved-neck vase (side view)
Somewhat inspired by some of Robert Lang’s recent work, this model has a twist that transitions from a 16-sided ‘circle’ to a square. Interestingly, the bottom edges of the square tube are approximately parabolic segments. The center doesn’t quite collapse cleanly, but it’s close enough for practical purposes. This twist is a bit more challenging to fold than the ones I’m used to. I might try incorporating some multi-shape twists like these into some of my more complex models.
In the past couple weeks, I’ve been experimenting with papers. Methylcellulose is commonly used in complex origami to size paper, making soft papers stiffer and easier to wet-fold, or to back-coat two sheets of paper and adhere them together.
Since the Elephant Hide paper I usually use doesn’t need to be sized, I didn’t try out methylcellulose until very recently. Since my designs need fairly stiff, thick papers, even adding methylcellulose isn’t enough to make some papers usable. But, if the pretty paper is thin enough, I can use methylcellulose to adhere it to Elephant Hide, and the double-layer paper folds essentially like a sheet of Elephant Hide.
This model is folded from a fairly thin sheet of marbled paper adhered to Elephant Hide. The marbled paper has a bit of texture, so it didn’t stick to the Elephant Hide quite as well as I had hoped, but I was still able to fold it into a relatively simple vase form.