I've shared some of my recursive crease patterns before here and there, but it occurred to me that I'd love to hear of what others have concocted even if it only exists in the aether. So if you'd care to describe your designs below, I'd be very happy to read about them. Crease patterns, written descriptions, 3D models of what it would look like given impossibly thin paper and an eternity are all welcome.
To start things off, the most frustrating recursive model I've come up with* is a diamond perpendicular to a plane:
Folded, two levels
Crease pattern, many levels
What it would look like with infinitesimally thin paper and a LOT of time
In theory, you can narrow the base of the diamond (where it touches the rest of the paper) to a point. Sadly, each time you half the size of the connecting corner, you double (maybe more?) the number of layers.
Folded for one iteration it looks pretty good. Folded for two, not so much. Anything beyond that tends to be a disaster.
Because these diamonds can be tessellated, I was hoping to do many of them from one sheet of paper, narrow the connecting corner and fold cranes out of them
Sadly, it is not to be.As a side note, the faces of the diamond are unfolded. So this could, in a perfect world, be made into a fractal (diamonds on diamonds on diamonds...) that was also tessellated.
* I've found out that Maekawa's Turkey has a similar structure. So independently invented, but not an original, I'm afraid.
