Phyllotaxis
the spirals are counted, not admired
Concept

Threshold — where it appears

A line drawn on a measured quantity to sort it into two groups. Every one in this collection is stated with the gap it sits in, because a line in an empty gap is a way of writing down a separation and a line through a continuum is a decision dressed as one.

Named by 2 essays across 2 fields — 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 The settling share at every rise, sampled two ways. How often a stem reaches a lattice, against the rise, at each of the four falloff exponents. The horizontal rule is the half share the wall is read at. At nine starting angles the four exponents cross it at rises spanning a factor of 1.96 and order themselves 2, 5, 3, 4; at twenty they span a factor of 1.18 and order themselves 5, 4, 2, 3. The ordering reverses and the spread collapses, so the conclusion that the exponents do not separate is confirmed and the numbers that had suggested otherwise were the coarser sampling's own error.

A wall that stopped moving

Four falloff exponents were reported not to move the rise below which stems stop reaching a lattice. Their measured walls spanned a factor of two and ordered themselves 2, 5, 3, 4. At twenty starting angles they span a fifth of one and order themselves 5, 4, 2, 3 — so the conclusion was right and its arithmetic was noise.

emergence · exponent

Named alongside it

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

Claim testingHonest limitsArtefactAzimuth gridBasinBoth wallsDisplacementFalloff exponentInteractionMeasurement errorNull modelReproducibility

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