Phyllotaxis
the spirals are counted, not admired
Concept

Hysteresis — where it appears

2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
100120140-3-2-1log₁₀ of the rise at the forkdivergence angle at the fork (°)137.508° — Fibonacci99.502° — Lucas13 forks, each solved for three equal families137.4730° and 99.5495°

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 10011012013014011.502falling rise, as −log₁₀divergence the stem is producing (°)137.51°, Fibonacci99.50°, Lucasseeded at 99.50°, rise 0.127/11 against 8/13

The rate decides the branch

Forty nodes of Lucas lattice, carried down to the same fine rise twice. Hurried, the pattern holds the Lucas ladder through three more forks at 99.5°. Given room, it abandons it at the first fork it reaches and walks to 8/13 at 137.5°. Same seed, same rise, two ladders — with a threshold between them at about ninety nodes per rung.

emergence · branch choice

Named alongside it

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

BifurcationBranchFibonacciLadderRepulsionRiseAttractorBranch selectionContinuityCritical rateInitial conditionMetastability

All concepts