Phyllotaxis
the spirals are counted, not admired
Concept

Surface of revolution — where it appears

2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
1231234rise exponent p, where the rise falls as z⁻ᵖratio between consecutive transitions along the axis5 surfaces, 16 measured transitionsworst disagreement 0.8%

The shape and the law

A cone's transitions are a factor of φ² apart and a disc's a factor of φ, and the temptation is to read the ratio as the shape. It is not. Five surfaces built and counted show that the ratio measures one exponent, and that the exponent is the shape multiplied by the way material arrives.

cylinder · shape exponent the meridiana conean ogivea convex head00.50011.50200.2000.4000.6000.8001along the meridian, as a fractionlocal exponent a(s)a = 1, a conedifferenced from each profile, not looked upogive 2.00 → 0.23

An organ has no single exponent

The previous phase measured that a surface whose circumference grows as a power of arc length puts its transitions a fixed factor apart, and checked it on five surfaces. Every one of them had a single exponent, and no organ does — a fir cone is an ogive, whose exponent runs from 2 at the tip to nearly 0 at the shoulder.

cylinder · varying exponent

Named alongside it

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

LadderOgiveParastichyRiseTransitionsArea fillingCapitulumConeCylinderDegeneracyElongationThe local exponent

All concepts