Phyllotaxis
the spirals are counted, not admired
Concept

Rising phyllotaxis — where it appears

A pattern whose parastichy numbers increase as the stem grows, because its rise is falling. It is the normal case rather than an exception, and it is where the question of whether a pattern can change branch actually lives.

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

The spiral counts, band by band, in one head. The same flower gives 13/21, 21/34, 34/55, 55/89 at different radii. A caption saying "34 and 55 spirals" is a statement about one annulus.

The counts change with radius

The same head gives 13 and 21 near the centre, 21 and 34 further out, 34 and 55 beyond that, and 55 and 89 at the rim. The transitions are at computable radii, and a photograph captioned with one pair is a statement about one annulus rather than about a flower.

lattices · Transitions A stem grown at 42 nodes per rung. 167 nodes, each placed where the repulsion from the ones below it was least, with the rise falling from 0.2 to 0.0045. Counted blind in a sliding window the pattern walks 1/2 → 2/3 → 3/5 → 5/8, and the marks are where its answer changed.

A pattern with a rate

Every lattice in the essays before this one is a static object indexed by a parameter, and a plant is not. Put the rise on a clock, place each node where the repulsion from the ones below it is least, and the object that comes out has a history — which is the first thing here that could disagree with the ladder.

emergence · Rising

Named alongside it

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

BranchRiseTransitionsAnnulusContinued fractionContinued fraction convergentDivergence angleFibonacciHistoryLattice offsetNodes per rungNoise

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