Phyllotaxis
the spirals are counted, not admired
Generator

how-many-specimens

The sample size at which each comparison reaches 90 per cent power at a 5 per cent false-positive rate, from the exact binomial rather than a normal approximation. The census question — do plants show consecutive Fibonacci pairs far more often than the geometry does — needs 4: 14.7% is the share of divergence angles giving a consecutive Fibonacci pair at a fine rise; 90% is what a grown history gives.
Every open question here needs under 34 specimensThe sample size at which each comparison reaches 90 per cent power at a 5 per cent false-positive rate, from the exact binomial rather than a normal approximation. The census question — do plants show consecutive Fibonacci pairs far more often than the geometry does — needs 4: 14.7% is the share of divergence angles giving a consecutive Fibonacci pair at a fine rise; 90% is what a grown history gives.plants show consecutive Fibonacci pairs far more…4and more often even than a coin weighted to a half14a conifer cone's rings are spaced as a cone rather…1multijugate patterns are a real minority rather than…34against 14.7%, if the truth is 90%needs: the pair, at a stated rungagainst 14.7%, if the truth is 50%needs: the pair, at a stated rungagainst φ² = 2.62, if the truth is φ^(2/1.88) = 1.67needs: three ring positions, to ±3%against 2%, if the truth is 15%needs: the pair; the whorl's symmetryspecimens neededexact binomial · α = 0.05 · power 0.91 to 34 specimens

Drawn at its defaults, in the survey this site has not done. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 6 essays

the blast radius of changing it

The claims, measured

What "whorled" was hiding

The expansion phase's census put 35% of divergences in a bucket labelled whorled and moved on. Opened, every pair in it is k and 2k — the coarsest rung of the ladder, repeated k times — and reading the census up to jugacy takes the Fibonacci share from 14.7% to 50.1% without describing a single extra plant.

 The pattern itself

Two at a time

Every counter on this site asks how far it is from element i to element i plus m, and that index is a claim that the elements arrived one at a time. For teasel, for Cephalaria and for a real minority of plants the claim is false — and what those patterns turn out to be is an ordinary lattice, wrapped twice.

 The claims, measured

How many plants would it take

Fourteen specimens separate the geometry's Fibonacci share from a coin weighted to a half. Four separate it from what a grown history gives. One fir cone measured at three rings settles whether its ladder is spaced as a cone's or an ogive's. The sample sizes are small, and that is the uncomfortable part.

 The claims, measured

The survey this site cannot do

Four phases of asking for a dataset, and it is still not here. What this phase can do instead is specify it — the fields, the sampling, the sizes, and which of this collection's claims each one would settle. Two of the four fields asked for turn out to be worth less than the asking implied, and one was never asked for at all.

 The claims, measured

The test a plant could settle

Every other open question in this collection is priced in tens of specimens, and one of them in a hundred and sixty. This one is priced in internodes on a single stem, and the number is fifty-six — because it is a statistic of one sequence rather than a share of a population.

 The claims, measured

What a quiet plant is worth

Almost every measurement gets easier as the effect gets larger. This one gets harder — a stem's divergence sequence stops carrying information about its noise at precisely the scatter where the noise becomes obvious. The specimens worth measuring are the ones that look least interesting.

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