Phyllotaxis
the spirals are counted, not admired
Concept

Island — where it appears

An enclosed run of one surviving family inside a band sweep, counted as an island when it is under three rises wide. The rule counts rises rather than distance, so halving a sweep's step can take an island out of the category without anything about the pattern having changed.

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

The rise at 0.005845 the coarse grid steps over, under offset 6 at both steps. Offset 6's cut drawn at every rise between 0.00596 and 0.00573, coarse above and fine below, with a cell per rise coloured by the family the cut leaves standing and pale where the cut recovers. It changes its answer 3 times at the coarse step and 5 times at half the step, and the gain is the single rise 0.005845, where the 4 family is kept with 8 on both sides. That island is 0.86 parts per thousand of the rise wide, against 1.47 for the smallest step the coarse grid takes anywhere on the band, so no coarse rise could have landed on it.

New islands or old edges

Halving a band sweep's step found two more changes of surviving family, and there are two quite different things they could have been. Every coarse change and every coarse island turns out to be carried by exactly one fine one, so the extra pair is a rise the coarse grid stepped over rather than a boundary it misplaced.

cylinder · Sweep resolution The 125 steps of the golden 8/13 band, in units of the grid they are rounded to. The sweep's rises are held to five decimal places, so every step it takes is a whole number of units of that fifth place. Each bar is how many of this band's 125 steps are that many units: 99 of 1, 26 of 2. One unit is 1.653 parts per thousand of the rise at the handover of 0.00605, against a nominal step of 2.00, so a sweep asked for at one part in a thousand would land on the same rise twice and the finer grid has to be laid at 7 places instead.

The last unmoved setting

Halving a band sweep's step is only a halving if the sweep steps where it says it does, and this one does not: its rises are rounded to five decimal places, so at one handover the grain is 1.65 parts per thousand against a nominal step of two. Moving the last setting nobody had moved found the setting was never what it was called.

cylinder · Sweep resolution

Named alongside it

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

ArtefactDiscretisationHandoverHonest limitsMeasurementRefinementResolutionRiseAblationClaim testingContact familyExtrapolation

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