Origami & Folding
what one sheet can do
Series

Inverse problem — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 4 patterns, one folded profile1/122/124/127/1225311/123/126/128/1225312/124/125/127/1225312/125/127/128/122531foldedthe layer counts under each band are the same in every row, and so are the widths

    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.

    part 1 · flat-folding
  2. 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.

    part 2 · flat-folding
  3. 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.

    part 3 · flat-folding

All series