Phyllotaxis
the spirals are counted, not admired
Generator

The Lucas 4/7 cut whole, beside the three bands cut before it

One row per wrecking offset on each band, one cell per rise, coarse on the left, with each band's width in proportion to the rises it holds. A pale cell is a rise at which that offset's cut recovers and has no survivor to report; a dark cell keeps one of the band's own counted pair and a warm cell keeps a family off it, so a change of answer is where the tone changes. The Lucas 4/7 is the test the branch account most needed: 86 rises, 774 stems, 144 wrecks across two offsets and not one change of the surviving family. Across the four bands drawn, 1347 cuts wreck of 5396 grown. The dashed rule on each row is that band's own handover, where its two contact steps change places.
The Lucas 4/7 cut whole, beside the three bands cut before it. One row per wrecking offset on each band, one cell per rise, coarse on the left, with each band's width in proportion to the rises it holds. A pale cell is a rise at which that offset's cut recovers and has no survivor to report; a dark cell keeps one of the band's own counted pair and a warm cell keeps a family off it, so a change of answer is where the tone changes. The Lucas 4/7 is the test the branch account most needed: 86 rises, 774 stems, 144 wrecks across two offsets and not one change of the surviving family. Across the four bands drawn, 1347 cuts wreck of 5396 grown. The dashed rule on each row is that band's own handover, where its two contact steps change places.

Drawn at its defaults, in the ladder, cut whole. 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

Stems and cones

The fourth band, cut whole

Three bands cut at every rise left one account of which bands change their answer standing, and the account was the one nobody had a reason to prefer. The band that would have killed it has now been cut, and it did not kill it.

 Stems and cones

Two bands that wreck nothing

The census that reads a band refuses two of the six, and the refusal is correct: a band with no wrecked cut has no surviving family, so it has no answer to change. Cutting them anyway turns a refusal into a measurement, and the measurement has a third tone in it that the census cannot see.

 Stems and cones

Six bands, one table

Every rung of this ladder that carries a handover now has a band grown on it and cut at every rise it holds, and four accounts of which bands change their answer are scored on all six at once. The survivor is right on every band that can test it, and the same table read one cell differently kills it.

 Stems and cones

The coarse design scored

Every claim this thread has made about an uncut band rests on a sample of nine rises, and its record was the argument for trusting it. Six whole bands close that record, and two of its six correct verdicts are correct only because there was nothing on those bands to find.

 Stems and cones

A wrecking set with a range

Which offsets wreck a stem was taken to be a property of the lattice, and every band cut whole has found it to be a property of the rise instead. Six bands turn that replication into a measured range, and the range is a factor of fifty-one.

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