Origami & Folding
what one sheet can do
Generator

The ratio of one term to the last

A generator in the what it costs to know library, called 7 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.

growth-ratio 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

The ratio of one term to the lastThe number of ways a strip of n stamps folds, divided by the number for n−1. The odd and even terms approach from opposite sides and both are still climbing at twelve stamps, which is as far as anybody has counted by this method. Whether the ratio has a limit at all is not known.2468101222.22.42.62.833.23.4stampsratio to the term beforeodd terms, from aboveeven terms, from belowfilled: computed here, to 9 stamps · hollow: 10 and 11 and 12, computed once and quoted4,536 foldings at 9 stamps

upTo: 9

The ratio of one term to the lastThe number of ways a strip of n stamps folds, divided by the number for n−1. The odd and even terms approach from opposite sides and both are still climbing at twelve stamps, which is as far as anybody has counted by this method. Whether the ratio has a limit at all is not known.2468101222.22.42.62.833.23.4stampsratio to the term beforeodd terms, from aboveeven terms, from belowfilled: computed here, to 9 stamps · hollow: 10 and 11 and 12, computed once and quoted4,536 foldings at 9 stamps

upTo: 9

The ratio of one term to the lastThe number of ways a strip of n stamps folds, divided by the number for n−1. The odd and even terms approach from opposite sides and both are still climbing at twelve stamps, which is as far as anybody has counted by this method. Whether the ratio has a limit at all is not known.2468101222.22.42.62.833.23.4stampsratio to the term beforeodd terms, from aboveeven terms, from belowfilled: computed here, to 9 stamps · hollow: 10 and 11 and 12, computed once and quoted4,536 foldings at 9 stamps

upTo: 7

The ratio of one term to the lastThe number of ways a strip of n stamps folds, divided by the number for n−1. The odd and even terms approach from opposite sides and both are still climbing at twelve stamps, which is as far as anybody has counted by this method. Whether the ratio has a limit at all is not known.2468101251015202530stampsratio to the term beforeodd terms, from aboveeven terms, from belowfilled: computed here, to 7 stamps · hollow: 10 and 11 and 12, computed once and quoted462 foldings at 7 stamps

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.

The answer is bigger than the question

A twelve-square strip of stamps is twelve numbers of input and 146,376 objects of output. No algorithm writes that faster than it can be written, so 'efficient' has to be measured against the answer rather than against the question — and in folding that is the normal case.

Where the exponent comes from

The number of ways a strip of stamps folds grows exponentially, and the base of the exponential is a number nobody has proved exists. The ratio of one term to the last climbs past three and is still climbing where the computation stops — which is the only structural handle anybody has on the sequence.

All the figures · The what it costs to know field · The patterns a reader can fold