Phyllotaxis
the spirals are counted, not admired
Generator

angles-against-positions

Each row is one stem at one rise. The left column is the parastichy pair counted from the coordinates; the right is the single number read out of the divergence angles alone, over 5 runs. On the Lucas ladder — 3/4, 4/7, 7/11 — the readout returns the smaller number too, so it is reading the lattice rather than Fibonacci. The last row is the one that matters: at a rise of 0.05 the positions give an unarguable 2/3 and the angles give 4, 23, 12, 2, 9 — all five wrong, and all five refused.
What the positions say, and what the angles sayEach row is one stem at one rise. The left column is the parastichy pair counted from the coordinates; the right is the single number read out of the divergence angles alone, over 5 runs. On the Lucas ladder — 3/4, 4/7, 7/11 — the readout returns the smaller number too, so it is reading the lattice rather than Fibonacci. The last row is the one that matters: at a rise of 0.05 the positions give an unarguable 2/3 and the angles give 4, 23, 12, 2, 9 — all five wrong, and all five refused.counted from the pointsread from the anglesgolden, rise 0.0323 / 535/5 clear · peak 0.72golden, rise 0.0135 / 855/5 clear · peak 0.59golden, rise 0.0058 / 1385/5 clear · peak 0.78Lucas, rise 0.0323 / 435/5 clear · peak 0.52Lucas, rise 0.024 / 745/5 clear · peak 0.45Lucas, rise 0.0087 / 1175/5 clear · peak 0.59golden, rise 0.052 / 34, 23, 12, 2, 9refused — peak 0.13 under 0.345 runs per rise · the readout sees a list of angles and nothing elsethe refusal is the gate working

Drawn at its defaults, in the count, read out of the angles. 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

The pattern itself

A counter that sees no positions

This site has counted spirals two ways, and both were handed coordinates. A third counter is handed a list of angles and nothing else. It returns one number instead of two, it refuses more often, and where it refuses it would have been wrong every time.

 The claims, measured

What the protractor has to be

The readout that names the parastichy number costs sixty internodes, which is cheap. It also needs every organ's position measured to better than a quarter of a degree, which is not — and the requirement follows from arithmetic rather than from care, so no amount of averaging relaxes it.

 Stems and cones

The order carries the count

Take the divergence angles off a stem, throw away every coordinate, and autocorrelate what is left. The result is periodic at the smaller parastichy number — peaks at it and at every multiple of it. A list of angles, with no picture and no position in it, carries the spiral count.

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