Phyllotaxis
the spirals are counted, not admired
Concept

Dispersion relation — where it appears

Which spatial frequencies a reaction–diffusion system amplifies, as a function of wavenumber. It sets the spacing a Turing pattern picks and by itself says nothing about the angle between successive organs.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Which patterns grow on a ring of circumference 1.40. Modes 4 to 15 have positive growth rates and mode 8 is fastest. Integrating the full equations from a disordered start gives 8 peaks.

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Turing's final work was on phyllotaxis and it was unpublished when he died.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 The angle between the first two peaks, for six starting disorders. The same equations, the same ring, six different starting perturbations: 177°, 47°, 109°, 151°, 47°, 133°. A spiral needs the angle between successive elements to be the same one each time, and a stationary ring does not supply that.

A ring cannot make a spiral

The peaks on a Turing ring do not all appear at once — there is a first and a second. But which two lead is decided by the starting disorder, so the angle between them comes out at 177°, then 47°, then 109°, then 151°. A divergence angle is a relationship that repeats, and this one does not.

mechanism · Ring limit Which hops survive one wall, the other, and both. One row per lattice. The last three columns are the lags whose hop the cut stem still holds, unchanged from a control that shares its history — the measurement that identifies what a wrecked stem has become. Removing a single wall always leaves something standing, which is what every single-organ cut in this collection does. Removing both leaves nothing at all on two of six lattices, including the coarse rung that no single removal can wreck. A stem that keeps no rigid hop is not a wrecked lattice with a slip in it; it is a stem that is no longer a lattice.

The rung that two organs wreck

On the coarse 3/5 stem both walls of the slot heal when removed alone and wreck when removed together — and the wreck keeps no rigid hop at all. Two of the six pairs in the design end at a destination single removals almost never reach.

mechanism · Both walls

Named alongside it

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

CylinderRateWhorlAblationActivator–inhibitorAnnulusAuxinBifurcationClaim testingControlDivergence angleEmergence order

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