Phyllotaxis
the spirals are counted, not admired
Generator

comb-ratio

The ratio of the second comb to the main one, for a kinematic lattice whose errors are inherited from its two contact neighbours, against how unevenly that inheritance is split. The horizontal line is where the placement rule's own stems sit, at 0.65. Weighted by distance — the coupling a d⁻³ interaction would give, which at this rise favours the 13-neighbour by 1.26 to one because the 13-hop is the shorter — the forgery sits at 1.46, well above the rule. It reaches the rule's value only at about 3 to one the other way, which is a factor of 4 against what distance supplies and in the opposite direction.
The two combs, in the proportions the rule gives themThe ratio of the second comb to the main one, for a kinematic lattice whose errors are inherited from its two contact neighbours, against how unevenly that inheritance is split. The horizontal line is where the placement rule's own stems sit, at 0.65. Weighted by distance — the coupling a d⁻³ interaction would give, which at this rise favours the 13-neighbour by 1.26 to one because the 13-hop is the shorter — the forgery sits at 1.46, well above the rule. It reaches the rule's value only at about 3 to one the other way, which is a factor of 4 against what distance supplies and in the opposite direction.0.4000.6000.80011.201.40-0.30100.1760.3010.4770.699how much more strongly the error is inherited from the 8-neighbour than from the 13-neighbourthe second comb's strength as a fraction of the main comb'sthe placement rule: 0.65equal combs1:21:11.5:12:13:15:1at 3:1 the ratio is 0.75kinematic lattice · 3 seeds a pointgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in what a disturbance's own structure can forge. It carries a slider over ratio, so the claim in its caption strip is restated at every stop rather than at one. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 5 essays

the blast radius of changing it

What a plant might be doing

Errors that pass between organs

An organ's neighbours are the ones eight and thirteen places back — that is what a parastichy pair is. So a disturbance transmitted by contact is correlated at exactly the two lags the readout examines, and it does not have to be told them. Driven into a lattice with no rule in it, it returns the counted pair on eight stems out of eight.

 What a plant might be doing

What a forgery has to know

A lattice with transported errors reproduces the comb and the pair, so one quantity is left: the two combs' relative strength. Weighted by distance the forgery puts more in the second comb than the first; the rule does the opposite. It matches only if the coupling is turned three to one towards the further neighbour, which no falloff supplies.

 Stems and cones

A harmonic is a step taken twice

The spectrum contains the larger parastichy number, their sum, and echoes of the smaller one, and no ranking of peak heights separates them. What separates them is arithmetic: a harmonic is a multiple of the spacing and a family is not, and the two kinds sit in different residue classes.

 The claims, measured

The control a survey would need

A comb no longer shows that a plant computes its pattern, so the survey this site has been specifying for five phases has to change. What it loses is its headline; what it gains is a measurement a botanist can actually make — six requirements, four of them already in the specification, and a quantity nobody has ever reported.

 Stems and cones

The comb was never the rule

A control is only as strong as the alternative it builds, and the previous phase built one that varied the rule while holding the disturbance fixed at independence. Five phases of the angle-sequence thread, with what each claimed and what still stands — and why the next evidence has to come from an intervention rather than from a longer stem.

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