Origami & Folding
what one sheet can do
Generator

The outline is mostly crease — the folded outline generator

A generator in the flat-folding library, called 7 times across 2 essays. Below: what it draws with nothing specified and with the settings the essays give it, what it checked while drawing, and everywhere it is used.

folded-outline is one function. Everything below was drawn by it when the site was last published, at settings taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and when the generator changes, this page changes with it.

With nothing specified

The outline is mostly creaseFor four folded patterns, the total length of edge with paper on one side and nothing on the other, split into the sheet's own raw edge and the creases. The raw edge is the minority everywhere: what a folded model shows the world is mostly fold, and the boundary of the paper has gone inside.patternraw edge against crease, by lengthpreliminary base8 panels29.3% rawMiura, 5 by 420 panels20.8% rawsquare twist9 panels26.7% rawYoshimura, 6 by 565 panels6.7% rawthe shaded part is the sheet's own edge; the rest of the outline is creasemeasured with a step of 0.001 of the sheet, and checked across a tenfold sweep of itevery length here is summed over the layers, so a buried edge counts for nothing

which: [preliminary, miura, twist, yoshimura], eps: 0.001

The outline is mostly creaseFor four folded patterns, the total length of edge with paper on one side and nothing on the other, split into the sheet's own raw edge and the creases. The raw edge is the minority everywhere: what a folded model shows the world is mostly fold, and the boundary of the paper has gone inside.patternraw edge against crease, by lengthpreliminary base8 panels29.3% rawMiura, 5 by 420 panels20.8% rawsquare twist9 panels26.7% rawYoshimura, 6 by 565 panels6.7% rawthe shaded part is the sheet's own edge; the rest of the outline is creasemeasured with a step of 0.001 of the sheet, and checked across a tenfold sweep of itevery length here is summed over the layers, so a buried edge counts for nothing

which: [miura, yoshimura], eps: 0.001

The outline is mostly creaseFor four folded patterns, the total length of edge with paper on one side and nothing on the other, split into the sheet's own raw edge and the creases. The raw edge is the minority everywhere: what a folded model shows the world is mostly fold, and the boundary of the paper has gone inside.patternraw edge against crease, by lengthMiura, 5 by 420 panels20.8% rawYoshimura, 6 by 565 panels6.7% rawthe shaded part is the sheet's own edge; the rest of the outline is creasemeasured with a step of 0.001 of the sheet, and checked across a tenfold sweep of itevery length here is summed over the layers, so a buried edge counts for nothing

which: [twist, yoshimura], eps: 0.001

The outline is mostly creaseFor four folded patterns, the total length of edge with paper on one side and nothing on the other, split into the sheet's own raw edge and the creases. The raw edge is the minority everywhere: what a folded model shows the world is mostly fold, and the boundary of the paper has gone inside.patternraw edge against crease, by lengthsquare twist9 panels26.7% rawYoshimura, 6 by 565 panels6.7% rawthe shaded part is the sheet's own edge; the rest of the outline is creasemeasured with a step of 0.001 of the sheet, and checked across a tenfold sweep of itevery length here is summed over the layers, so a buried edge counts for nothing

What it checked while it drew

Collected while it drew, not written by hand. The count is how many separate times that claim was put to the test.

Where it is called

Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all of them at once, and so would a correction.

The outline is mostly crease

The edge of a folded model is what a reader looks at, and almost none of it is the edge of the paper. Measured across five patterns, the sheet's own boundary accounts for between nothing and a third of the exposed edge; the rest is fold, and on a waterbomb tessellation the raw edge does not reach the outside at all.

The shadow does not name the pattern

A photograph of a folded model carries an outline and a thickness at every point of it, and that is the whole of what it carries. It is not enough. Crease patterns in genuinely different places fold to identical outlines with identical layer counts, and nearly a third of the folded objects a short strip can reach are reached by more than one pattern.

All the figures · The flat-folding field · The patterns a reader can fold