Origami & Folding
what one sheet can do
Concept

Inverse problem — where it appears

Recovering the cause from the effect — here, the crease pattern from the folded object. It is badly underdetermined: many patterns fold to one outline, and the part that would separate them is inside the stack.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as profile — the same set of essays touches all of them, so they are one junction rather than several.

what the outline and the thickness leave open, and what the order closesprofilesambiguousthe order settlesand does not3 creases on 12ths69166103 creases on 16ths1844712354 creases on 12ths23371692the last column is patterns that fold to the same object, so no better photograph reaches them

The order does not name it either

A photograph of a folded model carries an outline and a layer count, and that is not enough to recover the pattern. Hand the observer the layer order as well — everything the object physically is — and most of the ambiguity goes. Most. What is left are pairs of genuinely different crease patterns that fold to the same object, which no better photograph reaches.

flat-folding · Inverse problem 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

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.

flat-folding · Inverse problem

Named alongside it

The objects these essays reach for when they reach for this one.

ProfileDuo paperEvidenceFolded stateIdentifiabilityLayer orderLayer orderingStackingTwo-colourability

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