Phyllotaxis
the spirals are counted, not admired
Concept

Fibonacci share — where it appears

The share of a census of divergences that reads as consecutive Fibonacci numbers. It is usually quoted from the geometry rather than from plants, at a stated rise. It falls steeply as the rise falls, and how far depends on whether a pair means two hops or two families.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as generous reading — the same set of essays touches all of them, so they are one junction rather than several.

What the "whorled" bucket contains, at a rise of 0.008. 7 pairs, sharing 7 different factors, and every one of them is k and 2k: the second-shortest hop is the shortest taken twice. What the two-hop rule files as whorled is one family read twice, and no copies of anything.

What "whorled" was hiding

The earlier work'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 pair of the sequence, 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. By the lattice's own two families it moves nothing, and the share is 3.2% either way.

wrong · Jugate census Every report within three of 21 and 34, and what a census would call each one. Rows are the first count from three below to three above 21, columns the second about 34. One count away, 21/33 would be read as 3 × 7/11; One count away, 21/35 would be read as 7 × 3/5. A report in an unshaded cell shares no factor and belongs to no family.

A shared factor has two readings

A report whose two counts share a factor has been read two ways. One account says it is a miscount announcing itself, since a true ordinary pair cannot share one. The other says it is a plant grown k organs at a time, and that reading took a census's Fibonacci share from a seventh to a half. It is one piece of evidence, and nobody has compared the rates. Above the smallest pair, at least two of the four reports one count from a Fibonacci pair share a factor and carry a family's name: 21/35 reads as seven whorls of 3/5, and 33/55 as eleven. At a chance of 5 per cent that a count is off by one, with 5 per cent of plants truly whorled, a report with a shared factor is a true whorl less than half the time.

wrong · Jugate census

Named alongside it

The objects these essays reach for when they reach for this one.

CensusClassificationGenerous readingJugacyBijugateCoprimeFibonacciHonest limitsLadderMeasurement errorParastichy pairRise

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