Origami & Folding
what one sheet can do
Concept

Colour change — where it appears

A design technique that brings the reverse side of the paper to the front where it can be seen. Which panels can ever do it is fixed by the pattern's two-colouring, and how deep they are buried is a layer-ordering question.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

00.10.20.30.40.500.20.40.60.81flap width, as a fraction of the sheetarea showingthe two are equal at a thirdfront showingreverse showingtotal facemeasured on the folded state at 4 flap widths, and the marks are those measurements

Bringing the other side to the front

Paper has two sides and most models show one. A colour change shows the other, and it is not a crease problem — which panels can show the reverse is settled by the pattern's two-colouring, and what it costs is twice what it shows.

design · Colour change patternfootprint with both colours over itlayers thereThe preliminary base8 panels, 4 one way up and 4 the other100%8.0The Miura fold24 panels, 12 one way up and 12 the other100%9.2The square twist9 panels, 5 one way up and 4 the other65%4.1The hexagon twist13 panels, 7 one way up and 6 the other72%4.1The Yoshimura pattern65 panels, 32 one way up and 33 the other100%60.0Fold and cut — the triangle7 panels, 4 one way up and 3 the other4%6.4The tapered corrugation28 panels, 14 one way up and 14 the other100%8.4The waterbomb tessellation52 panels, 26 one way up and 26 the other100%31.1

Decided before the design

A colour change brings the reverse side of the paper to the front, and the usual account is that the two-colouring of the panels decides which panels are available. Measured on the site's own printed patterns, availability is not the constraint: both sides lie over more than ninety-nine per cent of most folded footprints. The other side is not scarce. It is under eight layers of paper.

design · Colour change the bar is the share of the footprint showing the side that started face upthe rest of it shows the other side, and neither is chosen by anybodyThe preliminary base0.3%2 of 8 panels in viewThe square twist47.4%7 of 9 panels in viewThe hexagon twist90.8%10 of 13 panels in viewFold and cut — the triangle100.0%1 of 7 panels in view · 2 statesa panel out of view from above is not hidden — it is under the pile, and turning the sheet over shows a different set

Which side arrives

A colour change is described as a choice: bring the reverse of the sheet to the front where the design wants it. On a pattern whose panels can be ordered, nobody chooses. The preliminary base shows the side that started face up over one part in a thousand of its own footprint, and two of its eight panels are the only ones in view at all.

design · Colour change the bar is the footprint, split by how deep the other side liesone layer downtwo layers downnot under this point at allThe preliminary base8 panels · 1 stateThe square twist9 panels · 1 stateThe hexagon twist13 panels · 1 stateFold and cut — the triangle7 panels · 2 statesa 2 × 2 Miura patch4 panels · 1 statea 3 × 2 Miura patch6 panels · 3 statesa 3 × 3 Miura patch9 panels · 6 statesa 4 × 3 Miura patch12 panels · 11 statesthe letter fold3 panels · 2 statescounted over every folded state and from both faces, so nothing here is one lucky pile

One sheet down

A colour change has been priced by how deep the pile is — eight layers over every point of the preliminary base, six on a small Miura. Ordered, the piles say something else: wherever the other side of the paper lies under a point, it is the next sheet down on every pattern with one folded state, and never more than two down on any. And relettering the same creases cannot reach it. Of 112 letterings of the preliminary base that fold, every one shows either the printed face or the whole face turned the other colour; the square twist's eight only turn its face round.

design · Colour change

Named alongside it

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

Design techniqueFolded stateLayer orderTwo-colouringLayer countConservationDesignDuo paperFootprintLayer orderingTwo-colourability

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