Phyllotaxis
the spirals are counted, not admired
Generator

which-junctions-say-anything

Above: how many junctions of a given asymmetry it takes to distinguish an exponent of 3 from an exponent of 2, at 2% measurement error on each radius. An even fork needs one; a junction whose small daughter is a twentieth of the large one needs 2195. Below: 50 junctions from each end of the range, on a synthetic tree built at exactly 3. The even forks return 3.01; the twigs return 1.69, with an interval no wider — because 47% of them measure as a parent thinner than its own larger daughter, and dropping those keeps only the half where the noise ran the right way.
The uninformative sample does not say so — it says something elseAbove: how many junctions of a given asymmetry it takes to distinguish an exponent of 3 from an exponent of 2, at 2% measurement error on each radius. An even fork needs one; a junction whose small daughter is a twentieth of the large one needs 2195. Below: 50 junctions from each end of the range, on a synthetic tree built at exactly 3. The even forks return 3.01; the twigs return 1.69, with an interval no wider — because 47% of them measure as a parent thinner than its own larger daughter, and dropping those keeps only the half where the noise ran the right way.1101001000100000.2000.4000.6000.8001daughter ratio — the smaller branch over the largerjunctions needed to tell Murray's rule from Da Vinci'san even fork — one is enougha twig — 2195the same tree, built at an exponent of 3, measured twicethe truth — 350 even forks3.0150 twigs1.692% error per radius · 47% of twigs impossiblemargin 0.11% against 2.8% noise

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 3 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

A sample that is confidently wrong

Fifty lopsided junctions from a tree built at an exponent of exactly 3 return 1.7, with an interval that excludes 3 and excludes 2 as well. The sample carrying almost no information does not give a wide answer — it gives a narrow wrong one, and the cause is a selection nobody applies on purpose.

 The claims, measured

What a summary throws away

Four statistics this collection has relied on turn out to be incapable of varying with the thing they describe — one is invariant to shuffling, one is fixed by a theorem, one is a parameter that stopped mattering, one is a fitted number selected into being wrong. In each case the second statistic was free and nobody had taken it.

All 114 generators