Phyllotaxis
the spirals are counted, not admired
Generator

ratio-by-colour

The ratio of the second comb to the main comb on stems grown by the placement rule and jostled by seven different disturbances, all at 0.25° of displacement per organ and all on the same rule. Independent errors and errors with a memory return 0.76–0.81, which is the value this site measured for the rule. A periodicity at the smaller parastichy number takes it down to 0.45; errors inherited from the contact neighbours take it up to 1.09, most of the way to the 1.24 a transported disturbance gives with no rule in it at all. So the quantity separates arrangements by how their errors are related, not by whether anything computed the positions.
The ratio follows the disturbance, not the ruleThe ratio of the second comb to the main comb on stems grown by the placement rule and jostled by seven different disturbances, all at 0.25° of displacement per organ and all on the same rule. Independent errors and errors with a memory return 0.76–0.81, which is the value this site measured for the rule. A periodicity at the smaller parastichy number takes it down to 0.45; errors inherited from the contact neighbours take it up to 1.09, most of the way to the 1.24 a transported disturbance gives with no rule in it at all. So the quantity separates arrangements by how their errors are related, not by whether anything computed the positions.second comb ÷ main comb, at 0.25° of displacementthe rule, 0.79no rule at all, 1.24independent0.80a memory, ρ = 0.50.78a memory, ρ = 0.90.76a memory, ρ = 0.970.81repeating every 80.45inherited, a = 0.51.02inherited, a = 0.71.095 stems a row · rise 0.005generated from a stated rule, not drawn to look right

Drawn at its defaults, in what the rule does with a coloured disturbance. 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

The ratio was never about the rule

One phase ago the comb was retracted as evidence that a plant computes its pattern, and one quantity was exempted from the retraction: the ratio of the two combs, which a placement rule and a transported disturbance divide differently. Drive seven disturbances through the same rule and the ratio spans 0.45 to 1.09. The exemption does not hold, and the angle sequence has nothing left.

 The claims, measured

The survey loses its second outcome

The specification written one phase ago names three results the survey could return, and the second — a ratio near or above 1.30, read as evidence against the placement rule — is the one that would have been worth publishing. It does not survive this phase. The ratio moves with where the plant sits between two transitions, and it moves again with the colour of the plant's own disturbance.

 Where the angle comes from

A disturbance the organs share

The previous phases put three kinds of noise into the placement rule and found the lattice fails at about the same recorded scatter whichever kind it was. None of them asked what happens when the displacements are correlated between organs. At equal displacement per organ, a lattice survives three times as much of a disturbance the organs share — and what a protractor records is the part they do not.

 Where the angle comes from

The disturbance that travels

If a lattice survives three times the displacement when the organs share it, then a disturbance passed between the organs that actually touch should be the gentlest of all — it is correlated at exactly the offsets the rule places against. It is the harshest. Half the displacement destroys what independent noise leaves standing, and the reason separates two things that had been one.

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