Phyllotaxis
the spirals are counted, not admired
Generator

what-the-ratio-hides

Three quantities across the same sweep of the rule's depth, each divided by its own value for the shallowest rule so that they share an axis. The wander rises by a factor of 3.7 as the neighbourhood goes from 3 organs to 182. The scatter between neighbouring divergences falls by 1.57, because that is the part of a disturbance a placement rule corrects and a deeper rule corrects it better. What is left — how many degrees of slow drift actually reach the divergences — changes by 1.20, from 1.52 to 1.82 degrees. The rule barely filters a drift at any depth.
The wander climbs because its denominator fallsThree quantities across the same sweep of the rule's depth, each divided by its own value for the shallowest rule so that they share an axis. The wander rises by a factor of 3.7 as the neighbourhood goes from 3 organs to 182. The scatter between neighbouring divergences falls by 1.57, because that is the part of a disturbance a placement rule corrects and a deeper rule corrects it better. What is left — how many degrees of slow drift actually reach the divergences — changes by 1.20, from 1.52 to 1.82 degrees. The rule barely filters a drift at any depth.012342.262.081.480.9030.477organs in the neighbourhoodagainst the shallowest rulewanderscatterdrift througha drift correlated over 33 organs · 3 seeds a pointdrift through: 1.52° to 1.82°

Drawn at its defaults, in how deep the rule looks. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 3 essays

the blast radius of changing it

What a plant might be doing

The window was not the neighbourhood

A placement rule corrects what is relative between neighbours and passes what moves them all together, so how much of a slow disturbance gets through should depend on how deep the neighbourhood is. The obvious knob is how many organs the rule sums over. Swept across a factor of six, it changes nothing at all — and a parameter that is not binding produces exactly the flat sweep a robust result produces.

 What a plant might be doing

The drift goes the other way

A rule that corrects what its neighbourhood shares should let through any disturbance slower than its own reach, and should suppress anything faster — a crossover, tracking the depth. Swept over a neighbourhood that changes by a factor of sixty, there is no crossover anywhere, and the deep rule passes nearly four times as much as the shallow one. The prediction is not weakly supported; it is backwards.

 What a plant might be doing

What the ratio was hiding

The statistic that says a rule sharpens a drift rises by a factor of nearly four across a sweep of the rule's depth. Undo the normalisation and ask instead how many degrees of drift actually reach the divergences, and the answer changes by a fifth. Nearly all of the effect was in the denominator, and the denominator is the thing the rule is good at.

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