Phyllotaxis
the spirals are counted, not admired
Concept

Auxin — where it appears

5 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
-0.075-0.050-0.02500.025510152025number of peaks around the ringgrowth rate of that mode8 counted8 predictedDₐ = 0.000008, D_h = 0.00064predicted 8, counted 8

Turing's last problem

Turing's final work was on phyllotaxis and it was unpublished when he died. Its core is a ring of cells and two diffusing substances, and the thing it does is select a number of peaks — which can be predicted from the equations before anything is integrated, and then counted from what the integration produces.

mechanism · reaction diffusion 10 peaks48 cells, transport up the gradient10 peaks, contrast 93%

A pump that works uphill

The mechanism that actually has molecular support behind it does not use a diffusing inhibitor at all. Cells move auxin towards whichever neighbour already has more of it, which is the opposite of what transport is supposed to do — and it produces a spacing from a field that started uniform to within six per cent.

mechanism · auxin 1201301401500255075100stepdivergence angle produced at that step (°)golden anglegrowth 0.40settled spread 0.00°

Droplets with no biology in them

Douady and Couder dripped magnetised ferrofluid into a dish of silicone oil, and got spiral phyllotaxis with Fibonacci parastichy numbers out of a system containing no cells, no genes and no plant. That is the strongest evidence the pattern is physics — and the clearest warning about what a model can claim.

emergence · analogue 120° — a third of a turn3 and 6 — whorled137.51°2 and 3 — Fibonaccirise 0.055 in both panelsthe counts decide, not the eye

What a mechanism would have to show

This site says of every model it draws that reproducing a pattern is not explaining it. That is easy to repeat and hard to make precise. Here it is made precise — a list of what an account of phyllotaxis would have to establish, with each item marked according to whether the models on this site establish it.

mechanism · mechanism claims the rule: compute the energy round the circle, take its minimum, place the nodefield noiseperturbs the energy, before65intact runs kept the branch1changed branchplacement noisedisplaces the node, after44intact runs kept the branch0changed branch — none didthe one that moved: 8/13 at 137.8°, 1.31° of scatter110 intact runs of 1601 of 66 against 0 of 44

Where the noise gets in

Ninety runs of noise applied after the rule has chosen, and not one changes branch. Fifty-six of noise applied to the choice itself, and one does. Only a disturbance upstream of the decision can restructure which nodes are neighbours of which — which is what a branch is.

emergence · noise entry

Named alongside it

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

RateRiseWhorlBranchMechanismMeristemRepulsionUnderdeterminationActivator–inhibitorAnnulusAttractorBifurcation

All concepts