Phyllotaxis
the spirals are counted, not admired
Concept

Both walls — where it appears

The design that removes each of a growing organ's two neighbours, then both, and reads how far the next organ moves in each case. The fourth cell is what it exists for: the pair removal usually costs far more than either wall alone, and on some rungs it costs nothing over the larger.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

What is the same at 0.00998 and at 0.00997. Six quantities read on the two rises the transition sits between. Five of them are identical: the two walls the slot has, the divergence the intact stem settles to, the block the cut opens, which of the three removals wreck the stem, and the lags the doubled cut leaves rigid. The sixth is how far the first organ placed after the doubled cut moves, and it goes from 163.59 to -9.14 degrees. The lattice is the same on both sides; where one organ goes is not.

A transition and not a slope

The question was whether a fourth cell's cost declines smoothly to nothing or falls in one step. It falls in one step, and the answer decides whether a word in the collection names something or is a threshold on a continuum.

cylinder · Both walls Where the doubled cut's run finishes, at every rise of the sweep. The divergence the wrecked run ends at, rise by rise. It takes only a handful of values and jumps between them at rises one part in a thousand apart, 4 times inside the 9 rises of the finest sweep alone — where the walls, the block, the intact stem's divergence and the rigid lags are all held. So the end of a wrecked run is not a stable quantity on this rung, and no statement about where the stem finishes is available on either side of the transition. The first organ's displacement is the reproducible half of the same measurement.

The end of a wrecked run

The obvious follow-up to a transition in where one organ goes is whether the stem also finishes somewhere different. On this rung the question has no answer: a wrecked run's final divergence takes four values and changes between rises a thousandth apart, three times inside a nine-rise sweep.

cylinder · Both walls The golden 5/8 rung swept at 27 rises, with each removal's cost. How far the first organ placed after a cut moves, at every rise the sweep visits, coarse on the left. Removing both walls costs far more than removing the larger one alone above a rise of 0.00998, and exactly what the larger one costs below it. The change happens in one step of the grid the ladder is named on: 163.59 degrees at 0.00998 and 9.14 degrees at 0.00997, which is a fall of 154.5 degrees for a change of one part in a thousand in the rise.

Where a slot loses a wall

Two rungs were reported to go free at 84 and 85 per cent of themselves — the second removal stops costing anything over the larger one alone. Three samples a rung cannot say whether that is a transition or a slope, and twenty-nine more say it is a transition one grid step wide.

cylinder · Both walls Where every wrecked run finishes, rung by rung. One row per rung of the ladder, one mark per cut cell of the slot design, placed at the divergence that run ended on. The open mark on each row is the divergence the intact stem of that rung settles to. On the Lucas 1/3 and golden 2/3 rungs every wrecked run finishes at the same value; on the golden 5/8 they finish at 13 values spanning 215 degrees. 27 cells recover, and each of those finishes at its own settled divergence to within 0.03 degrees.

The column nobody read

Every cell of the slot design carries where its run finished as well as how far its first organ moved. One rung's worth had been plotted and called unusable. Reading all eight says the endpoint is exact on two rungs, wanders on six, and is worst on the one it was read on.

cylinder · Both walls

Named alongside it

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

Claim testingHonest limitsSlotAblationDisplacementResolutionInteractionNegative resultRiseRungTransitionArtefact

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