Origami · Geometry · Algorithms
Computational Origami
The part I did not expect: that folding paper is also a branch of mathematics, and that a crease pattern is a kind of program.
1 · What it is
Computational origami asks what folding can and cannot do, and how to compute a fold. Which crease patterns collapse flat? What shape can one uncut square become? How would a machine plan the folds?
Two rules I keep coming back to at a flat-foldable vertex: the alternating angles have to sum to the same amount on both sides, and the mountains and valleys have to differ by exactly two.
2 · Stanford, summer 2025
I spent the summer of 2025 at Stanford's origami summer camp, which was the first time I saw folding treated as something other than a craft — as geometry, as an algorithm, as a research question.
3 · Folding patterns — a Miura-ori you can fold
The Miura fold collapses a whole sheet along one degree of freedom: move one crease and every other crease moves with it. Drag the sliders.
Width contracts to — of the flat sheet. One motion, the whole pattern — that is what makes it useful for solar arrays and folded maps.
Cyan creases fold toward you, magenta away.
4 · Geometry & mathematics
Polyhedra were the way in. Once you have folded an icosahedron out of thirty identical units you cannot un-see the symmetry group behind it.
5 · Algorithms & computation
The questions that interest me most are algorithmic: given a target shape, which crease pattern gets there, and how would you search for it?
6 · Experiments
Small things I try and mostly get wrong the first time — tessellations, curved creases, unit variations at unusual counts.
7 · Future projects
A crease-pattern editor of my own, and a proper study of what makes a modular unit lock.