Phyllotaxis
the spirals are counted, not admired
Concept

Autocorrelation — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
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 -0.20000.2000.4000.6000.5000.75011.251.50divergence 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 a quiet plant is worth

Almost every measurement gets easier as the effect gets larger. This one gets harder — a stem's divergence sequence stops carrying information about its noise at precisely the scatter where the noise becomes obvious. The specimens worth measuring are the ones that look least interesting.

wrong · survey spec -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

Named alongside it

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

Divergence angleMeasurementNoiseDiscriminationIdentifiabilityMeasurement errorSelf correctionSummary statisticCylinderEnsembleEvidenceThe placement rule

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