A crimper reducing a strip to nothing
crimp-reduction is one function. Everything below came out of it during this
build, at arguments 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.
At its defaults
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 by running this generator with a listener on the assertions, not written here. The count is how many separate times this build put that claim 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
Changing this generator changes every figure on this list, which is what makes the list worth publishing rather than keeping in a check script.
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.
Every generator · The what it costs to know field · The patterns a reader can fold