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.

Placeholder Notes, sketches and photographs from the camp to be added here.

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.

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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?

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6 · Experiments

Small things I try and mostly get wrong the first time — tessellations, curved creases, unit variations at unusual counts.

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7 · Future projects

A crease-pattern editor of my own, and a proper study of what makes a modular unit lock.

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