Phyllotaxis
the spirals are counted, not admired
Generator

the-band-decides-the-answer

Six bands of daughter ratio, 300 junctions in each, all from trees built at an exponent of exactly 3 with the same 2% measurement error. The median implied exponent falls from 3.00 at an even fork to 1.58 at a twig, and the share of junctions that have any exponent at all falls from 100% to 53% over the same range. The rule across the top is a single fit over 200 junctions spanning the whole range: 2.85. A mixed sample is safe because least squares already weights by leverage — 42% of it sits in the most symmetric band and 0.06% in the twigs. The sample that is not safe is the one a person can reach.
A tree built at an exponent of 3, measured band by bandSix bands of daughter ratio, 300 junctions in each, all from trees built at an exponent of exactly 3 with the same 2% measurement error. The median implied exponent falls from 3.00 at an even fork to 1.58 at a twig, and the share of junctions that have any exponent at all falls from 100% to 53% over the same range. The rule across the top is a single fit over 200 junctions spanning the whole range: 2.85. A mixed sample is safe because least squares already weights by leverage — 42% of it sits in the most symmetric band and 0.06% in the twigs. The sample that is not safe is the one a person can reach.11.5022.5033.50012345daughter ratio of the junctions measuredexponent implied, and the share of junctions that imply one0.9–1100%0.7–0.9100%0.5–0.799%0.3–0.578%0.15–0.356%0.05–0.1553%all 200 junctions together: 2.85the tree was built at 3bars are the share with any exponent · whiskers are the tenth and ninetieth percentilesmeasurement error 2%

Drawn at its defaults, in which junctions say anything. 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

Branching and transport

Which junctions say anything

Da Vinci's rule and Murray's law differ by 12% at an even fork and by a tenth of a per cent at a twig. So one even fork settles which is right, and two thousand twigs do not — a factor of two thousand across a tree, decided entirely by the shape of the junction and not by how carefully it is measured.

 Branching and transport

The band decides the answer

A fit over a whole tree's junctions returns the exponent the tree was built at, even though most of its junctions are from bands that on their own return 1.6. Least squares is already weighting by leverage. The dangerous sample is not the mixed one — it is the one a person can reach.

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