Phyllotaxis
the spirals are counted, not admired
Generator

jugate-stems

1-jugate at 137.51° counts 2 and 3; 2-jugate at 68.75° counts 2 and 4; 3-jugate at 45.84° counts 3 and 6. Every count shares the factor k, and dividing it out leaves an ordinary lattice: what a k-jugate stem is, exactly, is k copies of an ordinary one wrapped k times round.
three stems: 1, 2, 3 primordia at a time1-jugate at 137.51° counts 2 and 3; 2-jugate at 68.75° counts 2 and 4; 3-jugate at 45.84° counts 3 and 6. Every count shares the factor k, and dividing it out leaves an ordinary lattice: what a k-jugate stem is, exactly, is k copies of an ordinary one wrapped k times round.1 at a time2 and 3symmetry order 12 at a time2 and 4symmetry order 23 at a time3 and 6symmetry order 3divergences 137.51° · 68.75° · 45.84°counted 2/3 · 2/4 · 3/6

Drawn at its defaults, in whorls, and patterns with k at a time. It carries a slider over rise, so the claim in its caption strip is restated at every stop rather than at one. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 1 essay

the blast radius of changing it

The pattern itself

Two at a time

Every counter on this site asks how far it is from element i to element i plus m, and that index is a claim that the elements arrived one at a time. For teasel, for Cephalaria and for a real minority of plants the claim is false — and what those patterns turn out to be is an ordinary lattice, wrapped twice.

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