Phyllotaxis
the spirals are counted, not admired
Concept

Continuity — where it appears

Whether a pattern changes smoothly as a parameter is turned or jumps. A stem that walks the ladder continuously and one that jumps a rung are different claims about the tissue, and the difference is visible in a tracked run.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

What a divergence picked at random gives, at a rise of 0.100. Fibonacci pairs take 59.6% of the circle at this rise, and the share falls as the rise does. The claim that Fibonacci counts are what nature "prefers" needs the preference to come from somewhere, and it is not from the geometry being generous.

How often is it Fibonacci

The claim that plant spirals come in consecutive Fibonacci numbers is stated as a near-universal. Asked of the geometry, the answer collapses with scale — at a coarse rise 67% of divergences give Fibonacci pairs, and at a fine one 15%, with whorled and unnamed pairs taking the rest.

wrong · Frequency Two paths down the same tree. Both start at the same first fork. Keeping the larger family every time reaches 137.473°; one different choice reaches 99.549°. Neither angle is in the arithmetic — both are limits of a path.

The tree and the attractor

The dynamical model settles on the golden angle over a range of one parameter and on the Lucas angle outside it, and it cannot reach the low-growth end at all. The lattice tree reaches everywhere, has no dynamics in it, and produces the same two angles as limits of two paths. Two routes, one pair of numbers.

emergence · Branch tree Fibonacci at a rise of 4.8e-3, asked two ways. Choose a divergence at random and a static lattice at this rise gives a consecutive Fibonacci pair 10.8 per cent of the time. Start coarse at a divergence nobody chose, grow the stem down to the same rise, and it is 100 per cent of 16 runs. The geometry is not generous; continuity is.

Continuity from a coarse start

At a fine rise, one divergence in seven gives a Fibonacci pair. Grow a stem from a coarse start at a divergence nobody chose, down to that same rise, and sixteen runs out of sixteen end on 8/13. The earlier work's interpretation was that continuity does the work; this is the measurement it never had.

emergence · Continuity

Named alongside it

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

BranchRiseAttractorBranch selectionCensusFibonacciLadderRepulsionBifurcationConvergenceDivergence angleFrequency

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