Phyllotaxis
the spirals are counted, not admired
Concept

Frequency — where it appears

How often a named pair turns up, as a share of whatever is being counted. On this subject the answer depends entirely on the measure: a share of divergences on the circle, of plants collected, or of stems a rule settles on are three different numbers with no reason to agree.

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

What a divergence picked at random gives, at a rise of 0.100. Fibonacci pairs take 59.6% of the circle at this rise, and the share falls as the rise does. The claim that Fibonacci counts are what nature "prefers" needs the preference to come from somewhere, and it is not from the geometry being generous.

How often is it Fibonacci

The claim that plant spirals come in consecutive Fibonacci numbers is stated as a near-universal. Asked of the geometry, the answer collapses with scale — at a coarse rise 67% of divergences give Fibonacci pairs, and at a fine one 15%, with whorled and unnamed pairs taking the rest.

wrong · Frequency How often a random divergence reads Fibonacci, by the two shortest hops and by the lattice's two families. Thirty-six hundred divergences at each rise. At 0.12: 67.5 per cent by hops, 10.9 per cent without the pair 1/2, and 32.4 per cent by the lattice's families; At 0.03: 31.1 per cent by hops, 7.3 per cent without the pair 1/2, and 14.3 per cent by the lattice's families; At 0.008: 14.7 per cent by hops, 1.9 per cent without the pair 1/2, and 3.2 per cent by the lattice's families; At 0.001: 4.7 per cent by hops, 0.2 per cent without the pair 1/2, and 0.3 per cent by the lattice's families.

Most of the Fibonacci share was one family read twice

The census behind How often is it Fibonacci takes the two shortest hops at each divergence and calls them the pair. A pair of spiral families has to be two families, and the second-shortest hop is often the first taken twice in the same direction. That is the whole of the bucket once marked whorled, and it is most of the Fibonacci share too, since the pair 1/2 is one family read twice. Read by the lattice's own two families, the share at a rise of 0.008 is 3.2 per cent, not 14.7; at 0.12 it is 32 per cent, not 67.5; and Fibonacci's tenfold lead over Lucas at the finer rises is gone, 3.2 against 3.0.

wrong · Frequency

Named alongside it

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

CensusMeasureParastichy pairBranchBranch selectionClassificationContinuityDivergence angleHonest limitsLattice vectorsPriorRise

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