Phyllotaxis
the spirals are counted, not admired
Concept

Discrimination — where it appears

3 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
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 02468234exponent khow badly r₀ᵏ = Σ rᵢᵏ fails at that kk = 3127 junctionsfitted k = 3.000

Fitting the exponent

Assuming the exponent is three and reporting the error tells you how wrong the data is. Fitting the exponent and reporting what it comes out as tells you what the network is doing — and the machinery has to be shown returning something other than three, or it is not a fit.

branching · exponent

Named alongside it

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

FibonacciBranchCylinderDivergence angleLocal minimumParastichyRiseConeDa Vinci's ruleExponent fittingHandednessL-systems

All concepts