Origami & Folding
what one sheet can do
Concept

Design constraint — where it appears

A condition a design must satisfy that comes from somewhere other than the shape being made. The grid it is drawn on, the sheet it is cut from and the lines a strip may be slid into are all of that kind, and each is usually invisible in the arithmetic that prices the design, because the arithmetic measures what the constraint is blind to.

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

a strand of 7249 bases at 64 to a helixthe bar is the largest member of the family that is still buildablea square blockstopped by the strand's length100 helices · 88% of the stranda single rowstopped by the strand's length113 helices · 100% of the stranda comb of teethstopped by the routing5 helices · 4% of the stranda plusstopped by the routingno size works at allan L with equal armsstopped by the strand's length113 helices · 100% of the strand

Two ceilings

A DNA origami is limited by the length of one viral strand and by whether its helices can be visited once each in a single pass. Grown one step at a time, a square block runs into the first at a hundred helices and a plus runs into the second at five — so which limit a shape meets is decided by the shape and not by the chemistry.

biology · Molecular folding a 8 by 8 grid, spacing 0.125 — what each strip width does to itthe bar is how many times finer the grid becomes — one means unchanged0.1251x1 spacings — the grid is unchanged0.251x2 spacings — the grid is unchanged0.3751x3 spacings — the grid is unchanged0.06252xthe grid becomes 0.0625, 2 times finer0.15xthe grid becomes 0.0250, 5 times finer0.1325xthe grid becomes 0.00500, 25 times finer0.25xthe grid becomes 0.0250, 5 times finera width four per cent away from a spacing divides the grid by twenty-five; a width half a spacing away divides it by two

The width is charged in grid

A grafted strip may be any width at all and the bill in paper is exactly width times length, with no second term — which is what the first of these essays established, and is a statement about area. The grid is a different property of the same pattern and it is not conserved: a strip whose width is not a whole number of spacings puts every vertex past the cut onto a finer grid, and a width four per cent away from a spacing divides the grid by twenty-five where a width half a spacing away divides it by two. A width nearly right costs far more than one plainly wrong.

design · Grafting

Named alongside it

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

Box pleatingCrease patternDesign costDNA origamiGraftingGridHamiltonian pathParityRoutingScaffold

All concepts