Phyllotaxis
the spirals are counted, not admired
Generator

width-carries-the-denominator

n²·w, measured at the two larger of each denominator's three head sizes and averaged, for six Fibonacci fractions. Undivided it runs 1188, 1285, 2999, 7005, 9125, 14297 — a spread of 12.0. Divided by the denominator it runs 149, 99, 143, 206, 166, 161 — a spread of 2.1. So the law is w ≈ 150·q/n² to within a factor of two, and the previous phase's constant of 1,400 to 3,300 was three measurements of the small-denominator end of it.
The coefficient is not one numbern²·w, measured at the two larger of each denominator's three head sizes and averaged, for six Fibonacci fractions. Undivided it runs 1188, 1285, 2999, 7005, 9125, 14297 — a spread of 12.0. Divided by the denominator it runs 149, 99, 143, 206, 166, 161 — a spread of 2.1. So the law is w ≈ 150·q/n² to within a factor of two, and the previous phase's constant of 1,400 to 3,300 was three measurements of the small-denominator end of it.33.504divergence angle, as a fraction of a turnn²·w, the coefficient of the width law (logarithmic)11881285299970059125142973/85/138/2113/3421/5534/89spread 12.0 across the sixsix denominators · n²·wgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in the dip at a large denominator. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 2 essays

the blast radius of changing it

Packing and tiling

The background is not one sample

The dip in disorder at a rational angle is a comparison against a background, and the background was one measurement taken two tenths of a degree away. At 21/55 that lands seven thousandths of a degree from 13/34 — inside another rational's dip — and the comparison inverts. Fixed, the dip survives to a denominator of 89.

 Packing and tiling

The width carries the denominator

The previous phase measured three denominators, found the dip's half-width falling as the square of the head size, and could not say whether its coefficient depended on the denominator. Six denominators say it does: the coefficient runs from 1,188 at q = 8 to 14,297 at q = 89, and dividing by q flattens a factor of twelve into a factor of two.

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