crosswind-slice

At its defaults it draws the solution along a line across a flow at 30°. Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 1.96·10⁻²³ — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 8.9·10¹² times that value and changes direction 9 times; upwinding turns 1 time and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 50 nodes.

crosswind-slice is one function in lib/figures/supg2d.js — the tuned diffusion in two dimensions — exact along one axis, and the direction it does not go. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 1.96·10⁻²³ — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 8.9·10¹² times that value and changes direction 9 times; upwinding turns 1 time and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 50 nodes.

Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 1.95·10⁻³¹ and is that same double at all fifteen nodes — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 3.4·10²¹ times that value and changes direction 11 times; upwinding turns 1 time and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 48 nodes.

Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 6.92·10⁻¹⁴ — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 257 times that value and changes direction 7 times; upwinding turns 1 time and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 18 nodes.

Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 1.96·10⁻²³ — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 8.9·10¹² times that value and changes direction 9 times; upwinding turns 1 time and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 50 nodes.

Four curves along the anti-diagonal of the grid, which at 45° is exactly a line across the flow. The exact solution depends on the flow coordinate alone, so on this line it never rises above 5.59·10⁻⁷ — the region the layer has decayed to nothing by. The streamline scheme's answer there swings over a range 8.7 times that value and changes direction 0 times; upwinding turns 0 times and stays inside [0, 1] everywhere on the grid, where the streamline scheme leaves it at 13 nodes.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

14 distinct claims across 5 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

Across the library: the rule bites on 70 of 151 generators — 55 print a residual and 15 are exempt with a published reason; 81 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.