Phyllotaxis
the spirals are counted, not admired
Concept

Neighbourhood depth — where it appears

How many organs a placement rule actually responds to, counted as the number carrying most of the profile it minimises. It is set by how fast the inhibition falls rather than by how many terms a program sums, and confusing the two produces a sweep in which nothing moves.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

020406015295785organs in the loopwander at a block of 64independentℓ = 2.8ℓ = 9.5ℓ = 32.83 seeds a point · vertical bars are the spread between themnothing depends on the loop bound

The window was not the neighbourhood

A placement rule corrects what is relative between neighbours and passes what moves them all together, so how much of a slow disturbance gets through should depend on how deep the neighbourhood is. The obvious knob is how many organs the rule sums over. Swept across a factor of six, it changes nothing at all — and a parameter that is not binding produces exactly the flat sweep a robust result produces.

mechanism · noise colour 02550750102030how many organs the disturbance stays correlated overwander at a block of 64182 organs120 organs30 organs8 organs3 organsneighbourhood measured as the organs carrying 90% of the profileno crossover at any depth

The drift goes the other way

A rule that corrects what its neighbourhood shares should let through any disturbance slower than its own reach, and should suppress anything faster — a crossover, tracking the depth. Swept over a neighbourhood that changes by a factor of sixty, there is no crossover anywhere, and the deep rule passes nearly four times as much as the shallow one. The prediction is not weakly supported; it is backwards.

mechanism · noise colour 012342.262.081.480.9030.477organs in the neighbourhoodagainst the shallowest rulewanderscatterdrift througha drift correlated over 33 organs · 3 seeds a pointdrift through: 1.52° to 1.82°

What the ratio was hiding

The statistic that says a rule sharpens a drift rises by a factor of nearly four across a sweep of the rule's depth. Undo the normalisation and ask instead how many degrees of drift actually reach the divergences, and the answer changes by a fifth. Nearly all of the effect was in the denominator, and the denominator is the thing the rule is good at.

mechanism · noise colour

Named alongside it

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

AutocorrelationFalsifiabilityHonest limitsMeasurementNegative resultNoiseThe placement ruleRepulsionSelf correctionArtefactDiscriminationDrift

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