Phyllotaxis
the spirals are counted, not admired
Concept

Summary statistic — where it appears

5 essays name this object, across 4 fields. What follows is each of them, and the objects they name alongside it.
Lewis slope — golden head0.009the law says 0.25Lewis slope — random set0.231the law says 0.25Aboav a — golden head1.177the law says 1.2Aboav a — random set0.593the law says 1.2filled where the tiling obeys the law it is being judged by900 points in each tilingLewis explains 32% of the area spread at best

Two laws that want opposite tissue

Lewis's law and Aboav's relation are quoted side by side as properties of cellular tissue. Measured on the same two tilings they point opposite ways — the ordered head satisfies Aboav's with the textbook value of 1.18 and fails Lewis's completely; the random set does exactly the reverse.

tissue · cell laws 00.2500.5000.750100200300internodes counted on one stemsmallest difference in correlation the count can resolvethe difference to resolve — 0.7656 internodesmatched at 0.75° of scatterone stem, counted once

The test a plant could settle

Every other open question in this collection is priced in tens of specimens, and one of them in a hundred and sixty. This one is priced in internodes on a single stem, and the number is fifty-six — because it is a statistic of one sequence rather than a share of a population.

wrong · sequence -0.25000.2500.500123456lag, in nodescorrelation between a divergence and the one that many nodes latersampling band4 runs each · 243 divergences per runmatched at 0.75° of scatter

The sequence has a memory

Every measurement this collection has made of a stem's divergence angles throws the order away. A spread is invariant to shuffling. Put the angles back in order and there is a large correlation between one and the next — 0.54 with no noise at all — which is the rule correcting itself, and which nothing had looked at.

cylinder · sequence -0.20000.2000.4000.6000.5000.75011.251.50divergence scatter, in degrees — the one quantity a plant offerscorrelation between one divergence and the next4 runs per point · band ±0.13every point is a lattice

What one angle says about the next

A tenth of a degree of placement noise moves a stem's divergence scatter from 0.50° to 0.62°, which nobody would report. It takes the correlation between consecutive angles from 0.54 to below zero. The other two kinds of noise, at scatters where no measurement can separate them, leave it at 0.6.

cylinder · sequence field1.64°intact to 0.015, broken by 0.02jostle1.72°intact to 1, broken by 1.4placement1.42°intact to 0.8, broken by 13 runs per amplitudescatters 19% apart

The boundary belongs to the pattern

Three kinds of noise, in three incommensurable units, destroy a lattice at the same place — about a degree and a half of divergence scatter. The previous phase measured that of two kinds and called it a scale rather than a constant. With a third it looks less like a coincidence and more like a property of what a lattice is.

emergence · scatter tolerance

Named alongside it

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

Divergence angleMeasurementNoiseAutocorrelationEnsembleIdentifiabilityThe placement ruleSelf correctionBasinCylinderDiscriminationEquilibrium

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