Phyllotaxis
the spirals are counted, not admired
Generator

cut-reproduces

loop cut at 3/√h: 8/13 at 137.62° with 0.58° of scatter. exponential cut-off, 3: 8/13 at 137.58° with 0.50° of scatter. no cut at all: no lattice, 44° of scatter. The first two agree to 0.03° — the prediction held — and the third is what the same rule does when nothing cuts it.
One rule at p = 1, cut three waysloop cut at 3/√h: 8/13 at 137.62° with 0.58° of scatter. exponential cut-off, 3: 8/13 at 137.58° with 0.50° of scatter. no cut at all: no lattice, 44° of scatter. The first two agree to 0.03° — the prediction held — and the third is what the same rule does when nothing cuts it.02040130135140145divergence the stem settles on, in degreesscatter of that divergence over the last quarter323 nodes, rise 0.4 → 0.004filled: a lattice · open: none

Drawn at its defaults, in a neighbourhood written down as a claim. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 5 essays

the blast radius of changing it

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

Two shapes, one threshold

Read in the same unit, an exponential falloff and a gaussian one disagree about where the lattice ends by half. The quantity they agree on turns out to be one the previous phase measured for an unrelated reason — and it agrees with a bracket left by a sweep of a completely different parameter.

 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.

All 105 generators