Phyllotaxis
the spirals are counted, not admired
Generator

depth-definitions

How many organs the placement rule is looking at, as its falloff exponent is swept from 1.5 to 6, by four different definitions. Counting the organs that carry half the profile gives 33, 12, 3, 2, 1. Counting the organs that carry nine tenths gives 182, 120, 30, 8, 3. Counting the organs that carry ninety-nine hundredths gives 284, 263, 149, 54, 9. Counting the organs that carry the weighted mean lag gives 68, 45, 21, 14, 11. They disagree about the size of the neighbourhood by a factor of 10 — the widest moves by 61 times across the sweep and the narrowest by 6.1 — and every one of them falls as the exponent rises. So no choice among them changes which rule is the deeper, and no redefinition can turn a result about the depth around.
Four ways to count the rule's neighbourhood, and one orderingHow many organs the placement rule is looking at, as its falloff exponent is swept from 1.5 to 6, by four different definitions. Counting the organs that carry half the profile gives 33, 12, 3, 2, 1. Counting the organs that carry nine tenths gives 182, 120, 30, 8, 3. Counting the organs that carry ninety-nine hundredths gives 284, 263, 149, 54, 9. Counting the organs that carry the weighted mean lag gives 68, 45, 21, 14, 11. They disagree about the size of the neighbourhood by a factor of 10 — the widest moves by 61 times across the sweep and the narrowest by 6.1 — and every one of them falls as the exponent rises. So no choice among them changes which rule is the deeper, and no redefinition can turn a result about the depth around.131030100300half the profilenine tenthsninety-nine hundredthsweighted mean lag1.52346falloff exponent of the placement ruleorgans in the neighbourhoodrise 0.005 · 5 exponents · top lags 13, 8, 5, 21, 26 at every onegenerated from a stated rule, not drawn to look right

Drawn at its defaults, in the depth, in the wrong unit. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 4 essays

the blast radius of changing it

What a plant might be doing

Four ways to count a neighbourhood

How deep does the placement rule look? Counting the organs that carry nine tenths of its profile gives 182 down to 3 as the falloff steepens. Counting the ones that carry half gives 33 down to 1. The weighted mean lag gives 68 down to 11. The four disagree by an order of magnitude about the size and agree exactly about the order.

 What a plant might be doing

The nearest organ is not the nearest neighbour

Rank the terms of the sum the rule minimises and read off which organs the biggest ones belong to. At every falloff exponent from 1.5 to 6 the answer is the same five: lags 13, 8, 5, 21 and 26. The organ placed immediately before is not among them, and counting the neighbourhood in organs was the wrong unit.

 What a plant might be doing

The corner that does not move

Read as degrees of drift getting through rather than as a ratio, and compared seed by seed, the deep and shallow rules change hands. The share that goes to the deeper rule climbs from twenty-three per cent under white noise to ninety-four at a correlation length of a hundred organs — and the crossing sits at two or three organs whether the two rules differ by a factor of four or sixty-one.

 Where the angle comes from

Not the shorter of the two

If a damaged stem keeps one contact family standing, the obvious guess is that it keeps the nearer one. Across thirty wrecked offsets that is true twelve times and false seventeen, and on one lattice the two steps differ by a quarter of a per cent — where the words shorter and longer are doing no work at all.

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