Origami & Folding
what one sheet can do
Generator

A holed sheet against a solid one of the same area

A generator in the designing a base library, called 6 times across 1 essay. Below: what it draws at its defaults and at the arguments the essays give it, what it checked while drawing, and everywhere it is used.

hole-packing 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

A holed sheet against a solid one of the same areaThe longest flap a seeded search could pack onto a square with a hole in it, against the same search on a solid square holding the same amount of paper. The bar is the difference as a percentage; it is a comparison of two searches at one budget and not of two optima.the bar is how much longer a flap the holed sheet carriesboth sheets hold the same area of paper, so this is about arrangement2 flaps4.20%0.7213 against 0.69233 flaps2.00%0.5165 against 0.50634 flaps2.09%0.4983 against 0.48815 flaps-0.27%0.3164 against 0.31736 flaps1.07%0.2907 against 0.28767 flaps1.30%0.2540 against 0.25078 flaps0.73%0.2386 against 0.2369a bar to the left is the search doing worse on the holed sheet, which is a search result rather than a finding

view: "pair"

Two flaps either side of a hole reach furtherTwo flap tips a fixed distance apart, on sheets with a slot of increasing width between them. On solid paper each flap stops when the two discs meet; across a hole they may overlap, because everything they share is not paper.two tips 0.6 of a sheet width apartthe bar is how long a flap each can carrysolid paper0.300the discs meet halfwaya slot 0.1 wide0.35719% further than solid papera slot 0.2 wide0.40435% further than solid papera slot 0.3 wide0.46655% further than solid papera slot 0.4 wide0.50067% further than solid papera slot 0.5 wide0.55184% further than solid paperthe tips do not move; only the paper between them does

view: "against"

A holed sheet against a solid one of the same areaThe longest flap a seeded search could pack onto a square with a hole in it, against the same search on a solid square holding the same amount of paper. The bar is the difference as a percentage; it is a comparison of two searches at one budget and not of two optima.the bar is how much longer a flap the holed sheet carriesboth sheets hold the same area of paper, so this is about arrangement2 flaps4.20%0.7213 against 0.69233 flaps2.00%0.5165 against 0.50634 flaps2.09%0.4983 against 0.48815 flaps-0.27%0.3164 against 0.31736 flaps1.07%0.2907 against 0.28767 flaps1.30%0.2540 against 0.25078 flaps0.73%0.2386 against 0.2369a bar to the left is the search doing worse on the holed sheet, which is a search result rather than a finding

view: "pair", widths: [0.05, 0.15, 0.25, 0.35, 0.45, 0.55]

Two flaps either side of a hole reach furtherTwo flap tips a fixed distance apart, on sheets with a slot of increasing width between them. On solid paper each flap stops when the two discs meet; across a hole they may overlap, because everything they share is not paper.two tips 0.6 of a sheet width apartthe bar is how long a flap each can carrysolid paper0.300the discs meet halfwaya slot 0.05 wide0.3258% further than solid papera slot 0.15 wide0.38428% further than solid papera slot 0.25 wide0.44147% further than solid papera slot 0.35 wide0.48461% further than solid papera slot 0.45 wide0.54180% further than solid papera slot 0.55 wide0.55184% further than solid paperthe tips do not move; only the paper between them does

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.

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.

Spending the cheap paper

A hole makes a sheet cheaper by the square inch, because a flap against its rim claims only half a disc. Whether a design can spend that was left open, because no packing search here could express a region that is not paper. It can now, and the mechanism turns out not to be the discount at all: across a hole, two flaps may overlap, and two tips three fifths of a sheet apart carry flaps of 0.500 rather than 0.300.

Every generator · The designing a base field · The patterns a reader can fold