Phyllotaxis
the spirals are counted, not admired
Concept

Local minimum — where it appears

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
2 and 3rise 0.090 · divergence 137.51°counted 2 and 3, opposed

A stem is a cylinder

The sunflower is the photograph, and it is the hard case. Nearly all real phyllotaxis happens on a stem, where the geometry is a lattice on a cylinder with two parameters — and where the spiral counts, which on a disc change with radius, are the same the whole way up.

cylinder · stem lattice 21 and 34 spiralscounted, not assumed

Counting the spirals

Almost every claim about phyllotaxis is a claim about how many spirals run through a pattern, and the count is almost never done. It can be done from the points alone, by machinery that is never told what angle built them — and then a count of 34 is evidence rather than a restatement.

lattices · counting stem, lower third2 and 3stem, middle third2 and 3stem, upper third2 and 3disc, r = 0.18–0.3221 and 34disc, r = 0.45–0.6234 and 55disc, r = 0.82–0.9955 and 89stem at rise 0.050, disc of 1600 points, both at 137.51°counted from coordinates onlyone answer against three

Counting up the stem

The same counting machinery, pointed at a stem instead of a seed head, returns one answer three times where the head returned three answers. That contrast is a measurement rather than a preference, and it is the one the whole cylindrical argument rests on.

cylinder · stem count

Named alongside it

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

Divergence angleParastichyRiseCylinderDiscriminationFibonacciLadderBranchConeCylindrical latticeHandednessLattice offset

All concepts