Many years ago, I designed the origami Arrow Illusion–an arrow that points in the opposite direction when viewed in a mirror.  It’s probably the biggest “hit” among my designs.  Recently, CFC (an Origami community) had a monthly challenge to create optical illusions, and it featured Arrow Illusion as an example.  So, I thought I’d design another.

I went through several ideas, but ultimately settled on the Reutersvärd Triangle.  It’s similar to the better-known Penrose triangle, but was actually created independently by Oscar Reutersvärd in 1934–before the Penrose triangle.

Like the Penrose triangle, the Reutersvärd Triangle is just an illustration–it’s impossible to actually make something shaped that way.  And yet, you can find many very convincing 3D-printed implementations of the Reutersvärd Triangle.  I felt this was a sign that I needed to origamize it.  (Note that the Arrow Illusion, too, was inspired by 3D printing!)

Actually designing the thing was fairly challenging, and I went through over half a dozen prototypes.  Even once I got the basic form down, I tried many ideas to optimize for simplicity and stability.  The end result is so elegant that its instructions fit on a single page.  Note: if you try to fold this, I suggest trying the “easy” version first, and make one with just 6 pieces of paper. It will look like this:

How does the illusion work?  The cubes are actually inverted.  Although it pretends to be a collection of cubes pointing outwards towards the camera, they’re actually internal corners pointing inwards.  It’s… not very convincing when you have the physical object right in front of you.  It’s most convincing when you take a photo in ambiguous lighting, and then sometimes it helps to turn the photo upside-down.  The lighting of the cubes doesn’t match the shadows behind the model, which may have caused some of you to see through the illusion already.  But in case you don’t see it, here’s a photo from the side:

I’m saddened to hear that Meenakshi Mukerji recently died.  I almost had an opportunity to meet her at a convention, but there was a pandemic and it never happened.  I’d give her a lot of credit for getting me into modular origami, and many of my earliest models were from her books.  I love her work.  This is a simple model that I have folded many times; it can be found in Ornamental Origami.

This iconic model is one that we folded at the East Bay Origami Convention back in March.  It takes inspiration from Boice’s Head Empty model, which is a person in a coat and tie, with a cube for a head.  Taking that same idea to the extreme, now we have a little doll with a giant cube for a head.  It’s pretty hard to get a photo of the thing, because from any view from above, the giant head eclipses the rest of the body.  If you could see it from above, you would see that the cube is open on the top and in the back.

Boice has a video tutorial.  It’s easier than it looks, but you may want to start with large paper.  I think it’s a good introduction to the box pleating method.

The tricky part was getting it to stand up.  I chose the fold the feet a bit differently from the instructions, giving it giant duck feet.

A lot of origami paper is colored on the front, and white on the back, so you can make patterns by carefully exposing the front and back.  I’m vaguely aware of a subdiscipline within origami all about making shapes just with color change.  But I have very little experience with it, and don’t understand any of the design principles!  As far as I’m concerned, it’s basically magic.  Perhaps one day I’ll give a shot at designing something like this.

The instructions for this model are available on CFC.

I feel compelled to mention that I am not a coffee drinker.  I drink tea.

Last month I attended the East Bay Origami Convention, which is a small event near me.  Origami conventions are generally organized into sessions with an instructor teaching models.  This snail was part of a session that folded a few simple models by Mark Bolitho. (The instructor was not Bolitho, it was someone else.)  Basically anyone can sign up to teach anything, so sessions can be a bit of a mixed bag, but this one was very nice.

Origami spaces are rather interesting.  They’re extremely age-diverse from preteens to retired folks, and you can’t judge a person’s skill level from their age.  There are a variety of interests, with figurative origami (i.e. origami that represents various forms like animals) generally being most popular, but there are also people like me who are more interested in abstract stuff like modulars and tessellations.  Sadly modulars and tessellations tend to be less suited to convention sessions, because you can’t really fold them in one hour.

There are also dual tendencies towards complexity and simplicity, with people wanting to impress with their skill, but also appreciating elegance and accessibility.  I’m situated somewhere in the middle of that.  I’m a very non-competitive person, so the show-offiness of origami spaces can be a bit off-putting sometimes.  But I’m also quite interested in technique and in mathematics, so there’s some complexity that comes with that.

I have a few books by Meenakshi Mukerji, and one of them (Ornamental Origami) has these floral balls.  I found the Layered Petunia particularly inspiring, because I had this idea of changing the connections to make different shapes.  The unit wasn’t really strong enough to hold though, so I had to redesign the unit.

This is a recent model that I just finished last month.  I decided to submit this to the East Bay Origami Convention two weeks from now.

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