Phyllotaxis
the spirals are counted, not admired
Concept

Metastability — where it appears

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
10011012013014011.502falling rise, as −log₁₀divergence the stem is producing (°)137.51°, Fibonacci99.50°, Lucasseeded at 99.50°, rise 0.127/11 against 8/13

The rate decides the branch

Forty nodes of Lucas lattice, carried down to the same fine rise twice. Hurried, the pattern holds the Lucas ladder through three more forks at 99.5°. Given room, it abandons it at the first fork it reaches and walks to 8/13 at 137.5°. Same seed, same rise, two ladders — with a threshold between them at about ninety nodes per rung.

emergence · branch choice placement noisedegrees off the minimum00.250.50.7511.251.52field noisefraction of the barrier00.00250.0050.00750.010.01250.0150.02kept its branchchanged branchanother pairno latticeseeded 40 nodes of Lucas lattice · 10 runs per amplitude1 escape in 160 runs

Noise is not a slow rate

A stem seeded on the Lucas branch keeps it below ninety nodes per rung and abandons it above — which invites the objection that a real apex's fluctuations would knock it off regardless. Measured across a hundred and sixty runs of two independent kinds of noise, one escapes, at the amplitude where the pattern is already coming apart.

emergence · noise amplitude 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.

BranchNoiseRiseDivergence angleFibonacciLadderThe placement ruleRateAuxinBifurcationCritical rateEnsemble

All concepts