Concept

Negative result — where it appears

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
-0.500-0.25000.2500.50011.251.501.752nodes the stem spends per rung, log₁₀transition late by, in rungsone rung late8 rates · rise 0.4 → 0.0012worst mean lag 0.087 rungs

The lag that is not there

A pattern built out of its own history should hold its old parastichy pair past the point where a fresh lattice would have changed, and the gap should grow as the shoot is hurried. Over a fifteenfold range of rate it does not — every transition lands within a tenth of a rung of where the static ladder puts it.

emergence · tracking
00.2500.5000.750100.2000.4000.6000.8001candidate azimuth, in turnsenergy the rule minimises, scaled to its own rangeexponentialhard — a step, not a sloperise 0.02 · p = 1two cut-offs, one lattice

A hard edge is not a falloff

The prediction was that cutting the neighbourhood at three spacings would reproduce the pattern truncation had manufactured. It does — if the cut is smooth. A hard cut at the same distance produces no pattern at any width, and the reason is that it is the only one of the three whose neighbour set depends on where the candidate is.

emergence · truncation
loop cut at 3/√h, p = 133%27.78° of scatterexponential cut-off, p = 1100%0.68° of scatterexponential cut-off, p = 3100%0.82° of scatter6 runs each, separated by 0.2° of placement noisehalf-weight radius 1.5 spacings

The fragility belonged to the window

A pattern that exists only because the rule cannot see far was expected to be held together by that cut, and to fall over when nudged. It does — while the cut is a loop bound. Written down as a falloff at the same range, the same rule keeps every run under the same nudge, at a scatter an inverse-cube rule cannot be told from.

emergence · noise amplitude

Named alongside it

The objects these essays reach for when they reach for this one.

RepulsionArtefactCut offDivergence angleThe range of the interactionNeighbourhoodThe placement ruleRiseTruncationBranchDiscretisationEnsemble

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