Phyllotaxis
the spirals are counted, not admired
Concept

Exponent — where it appears

The power in the placement rule's falloff, which sets how quickly an organ's influence on the next one drops with distance. It is the parameter that decides how deep the rule's neighbourhood is, and sweeping it is how this collection asks what the rule is reading.

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

Two readings of what a stem is, and one of them is wrong. The same runs read twice. On the left is the pair counted from the point positions by machinery that is never shown a divergence angle; on the right is the pair read from the divergence sequence, which is the column the depth thread has been quoting. Every exponent's stems are counted at 5/8 spirals from the points. Read from the angles, the deepest rule's stems come back as something else at every seed, and a pair with a 8 replaced in it is not a near miss but a family whose step is several times as long. The settled divergence moves by 0.118 degrees across all five exponents, so the rules are on one lattice and the disagreement is a defect in one of the two instruments.

The pair read from the angles

Checking that a jostled stem is still the lattice its panel is about turned up a disagreement. Counted from the point positions every rule's stems return five and eight spirals; read from the divergence sequence, the deepest rule's stems come back as five and seven at every seed. The points are right, and this site's founding rule is why.

lattices · counting The same comparison at three sizes of disturbance. Each row is one panel: how many of six seeds the deeper rule beats the shallower one on, at six correlation lengths, on the lattice at a rise of 0.013. At the size of jostle the thread used, cells across the middle sit at six of six — the largest number the panel can print — so no feature could have appeared there whatever the lattice did, and the reading that this rise has no corner was a reading of that ceiling. Raised, the cells come down, and at the largest disturbance the panel shows a clean crossing: the deeper rule loses at white noise and takes every seed once the disturbance remembers itself for a few organs. The corner is there, and the flat middle was the instrument.

Six of six is not a measurement

A panel comparing two rules seed by seed reported the deeper one winning every one of six seeds at four correlation lengths out of six, and was read as a lattice with no corner in it. Six of six is the largest number the panel can print, so the flat middle was a reading of the ceiling — and raising the disturbance brings a corner out of it.

emergence · noise colour

Named alongside it

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

ArtefactAutocorrelationClaim testingHonest limitsMeasurementResolutionCounting blindCeiling effectContinued fractionControlCounting radiusDivergence angle

All concepts