Generator

truncation-manufactures

The top 220 nodes of two stems grown by an identical rule whose energy does not converge. Allowed to see 3/√h neighbours it produces 8/13 at 137.62° with 0.58° of scatter — a lattice no test on this site would question. Allowed 12/√h it produces 44° of scatter and no pattern. The truncation was doing the work.
The same rule at p = 1, cut off at two distancesThe top 220 nodes of two stems grown by an identical rule whose energy does not converge. Allowed to see 3/√h neighbours it produces 8/13 at 137.62° with 0.58° of scatter — a lattice no test on this site would question. Allowed 12/√h it produces 44° of scatter and no pattern. The truncation was doing the work.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°

Drawn at its defaults, in how far the rule reaches. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 6 essays

the blast radius of changing it

Where the angle comes from

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.

Where the angle comes from

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.

Where the angle comes from

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.

Where the angle comes from

A neighbourhood is a hypothesis

Every simulation of this kind stops summing somewhere. The previous phase found that where it stops decides what pattern comes out — so the stopping place is not a detail of the program but a claim about how far a primordium's influence reaches, and it should be written down as one.

Where the angle comes from

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.

Where the angle comes from

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.

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