Concept

Information — where it appears

The number of yes-or-no answers needed to say which of several possibilities a thing is: log₂ of their count, when all are allowed. Here it measures what a file must add to a crease pattern to fix its folded object — nothing on a pattern with one folded state, 3.46 bits on a four-by-three Miura with eleven.

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

the layer-order field for the printed patterns, filled in where it can bepairs is how many signs the field holds; varying is how many of them differ between folded statespatternpanelspairsstatesvaryingto recordThe preliminary base82810noneThe Miura fold24228not listed24 panelsThe square twist93610noneThe hexagon twist136610noneThe Yoshimura pattern652055not listed65 panelsFold and cut — the triangle721261.00 bitsThe tapered corrugation28282not listed28 panelsThe waterbomb tessellation52926not listed52 panelsa pattern past eighteen panels is not listed here, and those are the patterns anybody folds

The field is empty where it would say nothing

The interchange format for crease patterns has a field for the layer order and nothing ever fills it in. Filling it in where the folded states can be listed — four of the eight printed patterns, and Miura patches to twelve panels — finds that the preliminary base and both twists have exactly one folded state, so every one of the field's signs follows from the crease pattern and the field would record nothing a reader could not compute. The fold-and-cut triangle has two states. The Miura is different: every patch with three or more columns has several — three, six and eleven on the three-by-two, three-by-three and four-by-three — so on the pattern that gets built the field carries information from six panels up, and the field's size had been measured as log₂ of the panels' orderings, which on the preliminary base is fifteen bits for an object that has zero.

history · Notation
234567024681012columns (rows, for the two-column patches)folded statestwo rows high: 1, 3, 5, 7, 9, 11three rows high: 6, 11two columns wide: 1, 1, 1, 1, 1a strip two rows high has 2c − 3 states; every patch's states are one choice with that many answers

One choice with eleven answers

A folded state was proposed as a short list of free choices — which way a flap lies, where a rim panel sits — with the layer-order field's signs following from them. Listed exhaustively on every Miura patch small enough, the choices are never independent: every sign that varies is tied to every other through a shared panel, so the states are one choice with many answers. And there are more answers than the record said. The overlap test had a blind spot a third of a panel wide, and with it corrected the three-by-three Miura has six folded states, not one, and the four-by-three eleven, not five.

history · Notation

Named alongside it

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

Fold formatFolded stateLayer orderingNotationStacking

All concepts