Dispersion relation — where it appears
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Turing's final work was on phyllotaxis and it was unpublished when he died.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.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
CylinderRateWhorlActivator–inhibitorAnnulusAuxinBifurcationDivergence angleEmergence orderGrowth parameterInitial conditionInstability