Phyllotaxis
the spirals are counted, not admired
Concept

Annulus — where it appears

3 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Turing's final work was on phyllotaxis and it was unpublished when he died.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 0255075406080fraction of the head's radiusparastichy numbers found in a band there1000 primordia at the golden angle4 different pairs

The counts change with radius

The same head gives 13 and 21 near the centre, 21 and 34 further out, 34 and 55 beyond that, and 55 and 89 at the rim. The transitions are at computable radii, and a photograph captioned with one pair is a statement about one annulus rather than about a flower.

lattices · transitions the first of the four — 300 of its 899 pointsused to buildcountsrecovered137.508°55 · 89137.520°99.502°47 · 7699.500°151.100°31 · 81151.105°77.960°37 · 6077.960°worst error 0.012°counts in, angle outthe recovery never sees the angle

Recovering the angle from the counts

Build a head at a stated divergence angle, forget the angle, and get it back from the spiral counts alone. Four angles, worst error twelve thousandths of a degree — and the only thing that crossed between the two halves was a list of coordinates.

lattices · recovery

Named alongside it

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

BranchCylinderDivergence angleFibonacciActivator–inhibitorAuxinContinued fractionContinued fraction convergentCoprimeDispersion relationInstabilityInterval estimate

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