Phyllotaxis
the spirals are counted, not admired
Generator

after-the-cut

The divergences of a stem whose organ eight places back was removed, against the same stem uncut. It never returns. What it settles into repeats exactly every 8 organs — 47°, 96°, 137°, 273°, 138°, 271°, 230°, 272° — and holds that cycle for the whole 300-organ run, with a mean of 186° and a spread of 83°. A rule that corrects a displacement does not correct a deletion.
A cut eight back is never undoneThe divergences of a stem whose organ eight places back was removed, against the same stem uncut. It never returns. What it settles into repeats exactly every 8 organs — 47°, 96°, 137°, 273°, 138°, 271°, 230°, 272° — and holds that cycle for the whole 300-organ run, with a mean of 186° and a spread of 83°. A rule that corrects a displacement does not correct a deletion.100200300050100organs placed after the removaldivergence, in degreescycle of 8rise 0.005 · cut 7 backgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in take an organ away, and watch. It carries a slider over back, 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 5 essays

the blast radius of changing it

What a plant might be doing

The organ that was taken away

Every observable this site has is read off an arrangement that was finished before the reading began, and the last phase showed what that costs. So remove one primordium from a settled stem and place the next one against what is left. The rule has to answer. The rival account cannot, because in it no organ's position was ever computed from its neighbours.

 The claims, measured

The experiment this site can specify

For eight phases the outstanding item has been a survey — photographs, a protractor, hundreds of specimens — and it has not been done. The intervention is a different kind of ask, and a cheaper one: a needle, one apex, and a yes-or-no per ablation. Here is what it would cost, what it would settle, and the four ways it could come out.

 Stems and cones

The grid was in the number

The rule places each organ at the least of a profile sampled at a fixed number of azimuths, and every flat run on this site samples 384 of them — a step of 0.94°, against a disturbance of a quarter of a degree. The quantisation is the larger of the two, it is white, and it moves the discriminator from 0.79 to 0.62. The convergence study the last phase asked for, in the place it turned out to matter.

 Where the angle comes from

A rule that cannot heal a hole

The placement rule corrects itself against a displacement — that is what the lag-one correlation of −0.6 has been saying for three phases. It does not correct itself against a deletion. Which organ is removed decides whether the stem is back on its lattice in twenty-four organs or never, and the boundary between the two is sharp, reproducible and in the middle of the front.

 Where the angle comes from

The pattern the cut leaves behind

A stem that never recovers from a removal is not disordered. Its divergences settle into a cycle of eight angles and repeat it exactly for the rest of the run, and a counter reading the positions calls the result 8/16 — a two-jugate lattice. The rule has a second attractor at the same growth parameter, and an ablation is how you get to it.

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