Phyllotaxis
the spirals are counted, not admired
Concept

Interaction — where it appears

How much more a pair of removals costs than the two removals separately, with the intact stem as the origin. It is the fourth cell of a two-by-two less the sum of the other two, and where the second removal costs nothing it is a cancellation rather than evidence.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as transition — the same set of essays touches all of them, so they are one junction rather than several.

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 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

Named alongside it

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

Both wallsClaim testingDisplacementHonest limitsResolutionRiseSlotTransitionAblationArtefactAzimuth gridRung

All concepts