ratio-map 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 is a surface, not a number Poisson's ratio for a Miura fold across the whole design space: the panel slant along one axis, how far the sheet is folded along the other, every cell measured off the solved rigid folding by finite difference. Every value is negative and none of them is the same, which is the difference between a property of a material and a property of a mechanism. -0.02 -0.02 -0.03 -0.04 -0.06 -0.10 -0.19 -0.49 -0.05 -0.06 -0.07 -0.10 -0.15 -0.23 -0.43 -1.01 -0.10 -0.13 -0.16 -0.21 -0.30 -0.45 -0.81 -1.79 -0.20 -0.24 -0.30 -0.39 -0.53 -0.79 -1.36 -2.93 -0.34 -0.41 -0.50 -0.64 -0.85 -1.24 -2.10 -4.41 -0.54 -0.65 -0.79 -0.99 -1.31 -1.88 -3.13 -6.48 -0.80 -0.94 -1.14 -1.42 -1.87 -2.64 -4.36 -8.95 0.12 0.20 0.30 0.42 0.55 0.70 0.85 0.08 0.20 0.32 0.44 0.56 0.68 0.80 0.90 panel slant how far the sheet is closed what the map says every cell negative from -0.02 to -8.95 a factor of 535.6 a material has one value; this has a working point, and it is chosen darker means more negative
slants: [0.12, 0.2, 0.3, 0.42, 0.55, 0.7, 0.85], states: [0.08, 0.2, 0.32, 0.44, 0.56, 0.68, 0.8, 0.9]The ratio is a surface, not a number Poisson's ratio for a Miura fold across the whole design space: the panel slant along one axis, how far the sheet is folded along the other, every cell measured off the solved rigid folding by finite difference. Every value is negative and none of them is the same, which is the difference between a property of a material and a property of a mechanism. -0.02 -0.02 -0.03 -0.04 -0.06 -0.10 -0.19 -0.49 -0.05 -0.06 -0.07 -0.10 -0.15 -0.23 -0.43 -1.01 -0.10 -0.13 -0.16 -0.21 -0.30 -0.45 -0.81 -1.79 -0.20 -0.24 -0.30 -0.39 -0.53 -0.79 -1.36 -2.93 -0.34 -0.41 -0.50 -0.64 -0.85 -1.24 -2.10 -4.41 -0.54 -0.65 -0.79 -0.99 -1.31 -1.88 -3.13 -6.48 -0.80 -0.94 -1.14 -1.42 -1.87 -2.64 -4.36 -8.95 0.12 0.20 0.30 0.42 0.55 0.70 0.85 0.08 0.20 0.32 0.44 0.56 0.68 0.80 0.90 panel slant how far the sheet is closed what the map says every cell negative from -0.02 to -8.95 a factor of 535.6 a material has one value; this has a working point, and it is chosen darker means more negative
slants: [0.2, 0.35, 0.5, 0.65, 0.8], states: [0.1, 0.3, 0.5, 0.7, 0.9]The ratio is a surface, not a number Poisson's ratio for a Miura fold across the whole design space: the panel slant along one axis, how far the sheet is folded along the other, every cell measured off the solved rigid folding by finite difference. Every value is negative and none of them is the same, which is the difference between a property of a material and a property of a mechanism. -0.05 -0.07 -0.12 -0.25 -1.01 -0.14 -0.21 -0.33 -0.63 -2.24 -0.29 -0.40 -0.62 -1.14 -3.81 -0.48 -0.66 -0.99 -1.77 -5.75 -0.73 -0.98 -1.45 -2.54 -8.08 0.20 0.35 0.50 0.65 0.80 0.10 0.30 0.50 0.70 0.90 panel slant how far the sheet is closed what the map says every cell negative from -0.05 to -8.08 a factor of 169.6 a material has one value; this has a working point, and it is chosen darker means more negative
slants: [0.12, 0.3, 0.55, 0.85], states: [0.08, 0.32, 0.56, 0.8]The ratio is a surface, not a number Poisson's ratio for a Miura fold across the whole design space: the panel slant along one axis, how far the sheet is folded along the other, every cell measured off the solved rigid folding by finite difference. Every value is negative and none of them is the same, which is the difference between a property of a material and a property of a mechanism. -0.02 -0.03 -0.06 -0.19 -0.10 -0.16 -0.30 -0.81 -0.34 -0.50 -0.85 -2.10 -0.80 -1.14 -1.87 -4.36 0.12 0.30 0.55 0.85 0.08 0.32 0.56 0.80 panel slant how far the sheet is closed what the map says every cell negative from -0.02 to -4.36 a factor of 260.9 a material has one value; this has a working point, and it is chosen darker means more negative
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.
every one of 56 sampled ratios on the map is negative ×4
the map is drawn over at least two slants and two fold states, so it is a surface rather than a line ×1
the ratio varies across the map rather than holding constant, so it is a property of the fold state and not of the pattern alone ×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.
All the figures ·
The tessellations field ·
The patterns a reader can fold