Phyllotaxis
the spirals are counted, not admired
Generator

19 changes and 2 at the coarse step, 21 and 2 at half of it

The changes of surviving family each band makes, at the step the sweep has always used and at half of it. The golden 8/13 band goes 19 to 21 and the golden 5/8 band 2 to 2. Halving the step cannot lose a change, since the fine grid holds every coarse rise with the same answer; what it can do is find one, and it does so on one band and not on the other. So whether a tally is a floor or a total is a property of the band rather than of the sweep — a floor where there are islands narrower than the step, and exact where there are none.
19 changes and 2 at the coarse step, 21 and 2 at half of it. The changes of surviving family each band makes, at the step the sweep has always used and at half of it. The golden 8/13 band goes 19 to 21 and the golden 5/8 band 2 to 2. Halving the step cannot lose a change, since the fine grid holds every coarse rise with the same answer; what it can do is find one, and it does so on one band and not on the other. So whether a tally is a floor or a total is a property of the band rather than of the sweep — a floor where there are islands narrower than the step, and exact where there are none.

Drawn at its defaults, in the band at twice the resolution. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 3 essays

the blast radius of changing it

Stems and cones

A count or a floor

Nineteen changes of surviving family on the widest band have been quoted as a number since the band was cut, with nothing to say whether a finer grid would find more of them. Halving the step finds twenty-one there and nothing at all on the next band along.

 Stems and cones

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.

 Stems and cones

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.

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