Generator

Two things called folding, and only one of them has a local test

A generator in the folding nobody designed library, called 6 times across 2 essays. Below: what it draws with nothing specified and with the settings the essays give it, what it checked while drawing, and everywhere it is used.

two-counts 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

Two things called folding, and only one of them has a local testThe number of states against the number of units, on a log scale. Both grow exponentially and that is not the difference. The difference is that a crease pattern's states can be filtered by four conditions checked one vertex at a time, and a chain's cannot be filtered by anything local at all.246810012345units (creases, or joints)log₁₀ statesa chain, 3 states per jointa sheet, two letters per creaseat one vertex, 4 of 16 assignments survive four local conditionsthe sheet's count has a local test that removes 75% of it · the chain's has none

chainStates: 3, upTo: 10, sectors: [40, 110, 140, 70]

Two things called folding, and only one of them has a local testThe number of states against the number of units, on a log scale. Both grow exponentially and that is not the difference. The difference is that a crease pattern's states can be filtered by four conditions checked one vertex at a time, and a chain's cannot be filtered by anything local at all.246810012345units (creases, or joints)log₁₀ statesa chain, 3 states per jointa sheet, two letters per creaseat one vertex, 4 of 16 assignments survive four local conditionsthe sheet's count has a local test that removes 75% of it · the chain's has none

chainStates: 3, upTo: 10

Two things called folding, and only one of them has a local testThe number of states against the number of units, on a log scale. Both grow exponentially and that is not the difference. The difference is that a crease pattern's states can be filtered by four conditions checked one vertex at a time, and a chain's cannot be filtered by anything local at all.246810012345units (creases, or joints)log₁₀ statesa chain, 3 states per jointa sheet, two letters per creaseat one vertex, 4 of 16 assignments survive four local conditionsthe sheet's count has a local test that removes 75% of it · the chain's has none

chainStates: 3, upTo: 8

Two things called folding, and only one of them has a local testThe number of states against the number of units, on a log scale. Both grow exponentially and that is not the difference. The difference is that a crease pattern's states can be filtered by four conditions checked one vertex at a time, and a chain's cannot be filtered by anything local at all.234567801234units (creases, or joints)log₁₀ statesa chain, 3 states per jointa sheet, two letters per creaseat one vertex, 4 of 16 assignments survive four local conditionsthe sheet's count has a local test that removes 75% of it · the chain's has none

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.

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.

All the figures · The folding nobody designed field · The patterns a reader can fold