Phyllotaxis
the spirals are counted, not admired
Generator

contrast-is-the-invariant

The exponential's lattice ends at 3.63 spacings and the gaussian's at 2.25 — ranges 47% apart — and at those two ranges the contrast is 5.74 and 6.09, 6% apart. The band is what the exponent route leaves: 3.98 at p = 1, where the uncut rule makes nothing, and 7.63 at p = 1.25, where it makes a lattice.
Two shapes, two ranges, one contrastThe exponential's lattice ends at 3.63 spacings and the gaussian's at 2.25 — ranges 47% apart — and at those two ranges the contrast is 5.74 and 6.09, 6% apart. The band is what the exponent route leaves: 3.98 at p = 1, where the uncut rule makes nothing, and 7.63 at p = 1.25, where it makes a lattice.204012345range at which the interaction has halved, in local spacingsnear-shell contrast — the first shell's variation over the second'swhat the exponent sweep leavesp = 1 · shells 0–2 and 2–4 spacingscontrasts 6% apart, ranges 47%

Drawn at its defaults, in a neighbourhood written down as a claim. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 3 essays

the blast radius of changing it

Where the angle comes from

How far a primordium reaches

The placement rule's repulsion falls as an inverse cube because that is what two magnetised droplets do, and nothing about a plant supplies the exponent. Asking what it controls produced one tidy wrong answer and one measured right one — and the difference between them is the difference between a total and a variation.

 Where the angle comes from

Two shapes, one threshold

Read in the same unit, an exponential falloff and a gaussian one disagree about where the lattice ends by half. The quantity they agree on turns out to be one the previous phase measured for an unrelated reason — and it agrees with a bracket left by a sweep of a completely different parameter.

 Where the angle comes from

The fragility belonged to the window

A pattern that exists only because the rule cannot see far was expected to be held together by that cut, and to fall over when nudged. It does — while the cut is a loop bound. Written down as a falloff at the same range, the same rule keeps every run under the same nudge, at a scatter an inverse-cube rule cannot be told from.

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