Phyllotaxis
the spirals are counted, not admired
Generator

where-the-noise-gets-in

Intact runs only, from the whole amplitude sweep. Placement noise displaces the node after the rule has picked an azimuth: 14 runs, none of which changed branch at any amplitude that left a lattice. Field noise perturbs the energy profile the rule picks over, so it can move the minimum into a neighbouring gap: 1 of 17 did.
Only noise that arrives before the choice can change what is chosenIntact runs only, from the whole amplitude sweep. Placement noise displaces the node after the rule has picked an azimuth: 14 runs, none of which changed branch at any amplitude that left a lattice. Field noise perturbs the energy profile the rule picks over, so it can move the minimum into a neighbouring gap: 1 of 17 did.the rule: compute the energy round the circle, take its minimum, place the nodefield noiseperturbs the energy, before16intact runs kept the branch1changed branchplacement noisedisplaces the node, after14intact runs kept the branch0changed branch — none didthe one that moved: 8/13 at 137.8°, 1.31° of scatter31 intact runs of 481 of 17 against 0 of 14

Drawn at its defaults, in noise, and where it gets in. 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

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.

 What a plant might be doing

The noise that arrives through the neighbours

The two kinds of noise this site had were idealisations that bracket the rule's choice. The realistic disturbance is neither: a primordium is placed exactly, and then the organ grows, so by the time the next one forms its neighbours have moved. That is a third kind, and it is invisible in every measurement a plant offers.

 Where the angle comes from

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.

All 105 generators