Concept

Truncation — where it appears

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
0501000.2500.5000.7501growth parameter Gspread of the last 30 steps (°) — 0 means settledfilled dark: convergedthe usable range is stated, not implied

Where the model stops

Below a growth parameter of about 0.18 this implementation does not converge — the settled angle wanders over a hundred degrees however long the run. That is the range where the literature says the interesting behaviour lives, and it is worth a figure rather than a quietly chosen axis.

emergence · modellimit
-8-6-4-20distance from the tip, in node spacingsvariation ÷ nearest shell, log₁₀0–22–44–88–1616–3232–64a golden-angle stem at a rise of 0.004 · shells in units of √hnearest shell dominates by 1.1× at p = 0.5, 9733× at p = 3

How far a primordium reaches

The placement rule's repulsion falls as an inverse cube because that is what two magnetised droplets do, and nothing about a plant supplies the exponent. Asking what it controls produced one tidy wrong answer and one measured right one — and the difference between them is the difference between a total and a variation.

emergence · interaction range
cut at 3/√h8/13 at 137.62°0.58° of scattercut at 12/√hno divergence angle43.86° of scatterexponent 1 · identical but for the neighbourhood0.58° against 43.9°

A window that makes a pattern

A rule whose energy has no well-defined minimum produces a clean 8/13 lattice at 137.62°, with half a degree of scatter, when its neighbourhood is cut at three node spacings. Let it see twelve and the pattern is gone. Every simulation of this kind truncates something, and truncation manufactures exactly the result it is used to look for.

emergence · truncation

Named alongside it

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

RepulsionConvergenceDivergence angleLadderMeristemThe neighbour graphThe placement ruleRiseArtefactBranchCylinderDiscretisation

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