ratio-map 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
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 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.
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
Changing this generator changes every figure on this list, which is what makes the list
worth publishing rather than keeping in a check script.
Every generator ·
The tessellations field ·
The patterns a reader can fold