Phyllotaxis
the spirals are counted, not admired
Concept

Multijugate — where it appears

Having more than one organ at each step: a whorl of k at one height, each whorl turned by a fixed angle from the last. A multijugate pattern is an ordinary lattice wrapped k times, so its spiral counts share the factor k and each of its sectors is an ordinary pattern.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

three stems: 1, 2, 3 primordia at a time. 1-jugate at 137.51° counts 2 and 3; 2-jugate at 68.75° counts 2 and 4; 3-jugate at 45.84° counts 3 and 6. Every count shares the factor k, and dividing it out leaves an ordinary lattice: what a k-jugate stem is, exactly, is k copies of an ordinary one wrapped k times round.

Two at a time

Every counter in these essays asks how far it is from element i to element i plus m, and that index is a claim that the elements arrived one at a time. For teasel, for Cephalaria and for a real minority of plants the claim is false — and what those patterns turn out to be is an ordinary lattice, wrapped twice.

lattices · Jugacy The cells of a 2400-organ head grown 2 organs at a time that are not hexagons. Organs in pale points; five-sided cells and seven-sided cells marked. 330 of 1596 interior cells are not hexagons, lying on rings at 22.5, 36.5, each ring with its pattern repeated 2 times round the head.

A whorl moves a ring out and multiplies it

A head grown k organs at a time is an ordinary lattice wrapped k times, which predicts its defect rings with no measurement at all: each of an ordinary head's rings should appear at k times the radius, holding k times the cells, one copy in every sector. On eight-thousand-organ heads of two to five organs a whorl every ring read holds exactly that count, 110 fives where 55 would be and 105 where 21 would be, at the predicted radius to a tenth of a unit. Stagger the members of each whorl by the single organ's radius that Vogel's rule would give and the counts do not change, while a fifth to a quarter of the defects lose their partner one sector on.

lattices · Jugacy

Named alongside it

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

BijugateJugacyRotational symmetryCensusDefect ringGenetic spiralHonest limitsLatticeRiseSpecimenTopological defectWhorl

All concepts