Phyllotaxis
the spirals are counted, not admired
Generator

window-band

For each rung of the ladder, the range of lag windows in which the pair can be read: at least three times the smaller parastichy number, so the main comb has three teeth inside the window, and less than three times the larger, so the larger number cannot itself be a candidate spacing. The band is [15, 24) at 5/8, [24, 39) at 8/13, [39, 63) at 13/21. It is non-empty at every rung, because it is empty only when the larger number is no larger than the smaller. The line at 30 is the window the previous phase used everywhere: it sits inside the 8/13 band and outside the 13/21 one, which is what was mistaken for a ceiling.
Every rung has a window it can be read inFor each rung of the ladder, the range of lag windows in which the pair can be read: at least three times the smaller parastichy number, so the main comb has three teeth inside the window, and less than three times the larger, so the larger number cannot itself be a candidate spacing. The band is [15, 24) at 5/8, [24, 39) at 8/13, [39, 63) at 13/21. It is non-empty at every rung, because it is empty only when the larger number is no larger than the smaller. The line at 30 is the window the previous phase used everywhere: it sits inside the 8/13 band and outside the 13/21 one, which is what was mistaken for a ceiling.runglag window, in internodes0153045605/8rise 0.0131524read at 218/13rise 0.0052439read at 3013/21rise 0.00193963read at 45the default window: 30three teeth in, the larger number outgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in the rung, the window and the sample grid. 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

The second comb

The autocorrelation of a divergence sequence has peaks at the smaller parastichy number and at every multiple of it. It also has a second set of peaks, at the same spacing, offset by the difference of the pair — so a list of angles with no coordinate in it returns both numbers rather than one.

 Stems and cones

The rung was not the instrument

The previous phase said the pair readout has a ceiling one rung above where it works, that this is arithmetic rather than statistics, and that no amount of stem fixes it. The arithmetic is right and gives a band of lag windows that is never empty; what was actually stopping the reading was an eight-node seed and a grid of 384 azimuths.

 Where the angle comes from

What a sample grid decides

The rule takes its minimum over 384 sampled azimuths, and that number has been a constant since this site's first commit. Tripling it changes nothing at the two rises the collection argues from — five runs of five, identical readings — and changes which answer appears at the one rise published as having no answer. A parameter of the program, measured rather than assumed.

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