A crimper reducing a strip to nothing
crimp-reduction is one function. Everything below was drawn by it when the site was
last published, at settings taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and when the generator changes, this
page changes with it.
With nothing specified
creases: [0.2, 0.4, 0.6, 0.8], assignment: "MVMV"
creases: [0.2, 0.3, 0.65, 0.7], assignment: "MVMV"
creases: [0.4, 0.5], assignment: "MV"
What it checked while it drew
Collected while it drew, not written by hand. The count is how many separate times that claim was put to the test.
- each crimp takes exactly two creases out of the strip and leaves no segment of negative length, and the 2 of them run the strip down to nothing left to fold ×2
- each crimp takes exactly two creases out of the strip and leaves no segment of negative length, and no sequence of crimps reduces this strip at all, which the ladder shows by stopping ×1
Where it is called
Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all of them at once, and so would a correction.
A machine that can only crimp
Change the atom and the whole picture changes. A machine whose single move folds two adjacent creases at once reaches strips no simple-fold machine reaches, is defeated by strips they handle easily, and cannot fold an odd number of creases at all — for reasons that are pure arithmetic.
The cost is in the coincidences
How big an instance is, is what a hardness statement is about, and it is the weaker predictor of what deciding one costs. Hold the degree fixed and vary only how many of a vertex's sectors are equal: the work of deciding it rises by a factor of nearly three, against a factor of two for doubling the number of creases. The expensive instances are the ones a designer draws on a grid.
All the figures · The what it costs to know field · The patterns a reader can fold