Origami & Folding
what one sheet can do
Generator

Three observers

A generator in the flat-folding library, called 7 times across 1 essay. 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.

photo-observer 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

Three observersEvery crease pattern of 4 creases on a grid of 12ths that folds flat, grouped by the outline it folds to. Of the groups holding more than one genuinely different pattern, how many each observer can separate.what the observer is givenambiguities separated, of 71the outline alonewhat a silhouette carries0the outline and the colourwhat a photograph of duo paper carries, from both sides0the complete layer orderwhat taking the model apart carries69the middle row is what anybody can actually see, and it is the top row

view: "ladder", k: 4, g: 12

Three observersEvery crease pattern of 4 creases on a grid of 12ths that folds flat, grouped by the outline it folds to. Of the groups holding more than one genuinely different pattern, how many each observer can separate.what the observer is givenambiguities separated, of 71the outline alonewhat a silhouette carries0the outline and the colourwhat a photograph of duo paper carries, from both sides0the complete layer orderwhat taking the model apart carries69the middle row is what anybody can actually see, and it is the top row

view: "parity"

The colour is decided before the foldA strip of paper coloured on one side, with the segments the creases cut it into. Which side each shows alternates along the strip, and no letter, no crease position and no stacking changes it.12345678the strip, before it is foldedthe colours alternate because the direction of travel reverses at every creaseso the palette of the folded model is fixed by the number of creases alone

view: "sides", creases: [0.08333333333333333, 0.4166666666666667, 0.5833333333333334, 0.8333333333333334], assignment: "MMVV"

What the camera seesA folded strip of paper coloured on one side, drawn as its outline with the side showing at each point of it from above and from below. Both sides are visible from above, which is what makes the colour an observation rather than a constant.24312from abovefrom belowlayers over each bandcreases at 0.08, 0.42, 0.58, 0.83, lettered MMVVthe two rows are the two photographs an observer can take

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.

Which side is showing

Two earlier rungs asked what a folded object records about the pattern that made it, first from its outline and then from its complete layer order. Neither observation is one anybody can make. A photograph of duo paper carries the outline, the thickness and the colour showing at every point — and over the whole census the colour separates nothing at all.

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