Phyllotaxis
the spirals are counted, not admired
Generator

basin-by-exponent

Each row pools one exponent's whole column — every rise, every starting angle — into one share, with a bar an error either side of it. Pooling is what makes the comparison possible: a single cell is 9 runs and carries an error of about 0.17, which is three times the whole spread between the four exponents. Pooled, the four sit at 30/72, 31/72, 29/72, 27/72 — a spread of 0.056 against an error of 0.058. Nothing in the falloff moves the basin. A five-angle version of the same sweep gave a clean monotone trend, which is what a null looks like when it is sampled too thinly.
The share of starting angles that reach a lattice, by exponent. Each row pools one exponent's whole column — every rise, every starting angle — into one share, with a bar an error either side of it. Pooling is what makes the comparison possible: a single cell is 9 runs and carries an error of about 0.17, which is three times the whole spread between the four exponents. Pooled, the four sit at 30/72, 31/72, 29/72, 27/72 — a spread of 0.056 against an error of 0.058. Nothing in the falloff moves the basin. A five-angle version of the same sweep gave a clean monotone trend, which is what a null looks like when it is sampled too thinly.

Drawn at its defaults, in the wall, against the falloff. 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

Where the angle comes from

A steeper rule walls nowhere else

The account of the wall at the fine end was that the basin narrows because the neighbourhood deepens, which predicts a steeper falloff walling somewhere else. Grown at four exponents, the four columns settle 30, 31, 29 and 27 of 72 — a spread of 0.056 against an error of 0.058.

 Where the angle comes from

The clock a share cannot see

Settling takes nothing to 290 organs, and four rounds of this collection have carried that as a property of the rule. At a steeper falloff the slowest is 808 — and not one of the 72 pairs of runs settles at 3,200 organs after failing at 1,200, so the fine end is still a wall.

 Where the angle comes from

Destinations only a steep rule reaches

A settled stem's divergence is the sharpest instrument in the sweep and the cheapest: it is already in every run, it does not average, and it is read on one grid at every exponent. Exponents 4 and 5 reach 42.3°, 47.9° and 148.1°, and the two shallower ones reach none of them.

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