Articles and Tutorials — math
Academic Origami Publications
Posted by Madonna Yoder on
My introduction to the possibility of a career in origami came during the Geometric Folding Algorithms class I took in my last semester at MIT.
This blog post features a list of academic articles I’ve has published since starting Gathering Folds.
Tiling-Based Origami Tessellation Design
Posted by Madonna Yoder on
Origami tessellations are infinitely repeating patterns folded from a single sheet of paper.
My designs are in the twist-based style and I fold my patterns one twist at a time whenever possible.
Siren's Call Origami Tessellation
Posted by Madonna Yoder on
There are some patterns that when I see them, I know I have to fold them.
Usually I keep a queue of about 10 of these patterns, but sometimes one skips to the front of the line.
Siren's Call is one of those.
Dancing Pyramids Origami Tessellation
Posted by Madonna Yoder on
A Whole Lot of 3 Sometimes it can be hard to tell what's 3 and what's 6. Now this may sound confusing - how can you not know the difference between 3 and 6? But when there's 6 things, with alternation between each one, is it 3 or is it 6? In terms of rotational symmetry, the answer is 3. In terms of twists in a loop, the answer is 6. And to make matters worse, you can't look for 3-fold symmetries around the point in question to decide - they're all going to be 3-fold in either case!...
Hybrid Closed Islands Origami Tessellation
Posted by Madonna Yoder on
Tiling Surprise Believe it or not, Hybrid Closed Islands has the same tiling structure as Robin Scholz's Celtic Circle. Both of these tessellations feature twists with six pleats (hexagon twists) surrounded by twists with three pleats (triangle twists) and vice versa. However, when you look at Hybrid Closed Islands it's easy to see only triangles - because the six-pleated twists only have three-fold rotational symmetry. Centering Choices In this tessellation, I have three equivalent choices of what to put in the center, and whatever I put in the center will be emphasized in the pattern. Each of these three...
Rotated Grids Challenge Winner
Posted by Madonna Yoder on
The challenge winner is Dirk Eisner!
Rotated Grids Challenge
Posted by Madonna Yoder on
Here is my challenge to you: fold a tessellation on an appropriately rotated grid and post a photo before May 12th for a chance to win a unique mini suncatcher, folded and framed by me!
Rotating Grids in Squares and Hexagons
Posted by Madonna Yoder on
You don’t have a laser cutter or Cricut scorer, but you still want to make stunning tessellations without guessing and iterating over and over. The good news is that there’s a fairly simple solution - rotated grids!