Phyllotaxis
the spirals are counted, not admired
Generator

where-a-wreck-goes

The settled divergences reached by every arrangement that never repairs, at each size of cut, on a stem whose parastichy pair is 5/8, counted rather than assumed. Each point is one destination and its size is how many arrangements reached it. Cuts of one organ and cuts of five land in the same handful of places; the largest cut invents nothing the smallest did not already reach. The dashed line is the mirror of the divergence the stem was cut from — the place a coarser stem goes when two organs are taken from it — and no arrangement at any size comes within 12 degrees of it.
Where a wrecked stem settles, whatever was taken from itThe settled divergences reached by every arrangement that never repairs, at each size of cut, on a stem whose parastichy pair is 5/8, counted rather than assumed. Each point is one destination and its size is how many arrangements reached it. Cuts of one organ and cuts of five land in the same handful of places; the largest cut invents nothing the smallest did not already reach. The dashed line is the mirror of the divergence the stem was cut from — the place a coarser stem goes when two organs are taken from it — and no arrangement at any size comes within 12 degrees of it.the mirrorcut fromone organ2 wreckedtwo organs18 wreckedthree organs51 wreckedfour organs112 wreckedfive organs63 wrecked140°180°220°260°settled divergence after the cutrise 0.013 · cut from 136.781°mirror at 223.219°

Drawn at its defaults, in how many organs it takes. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 4 essays

the blast radius of changing it

Where the angle comes from

One turn per survivor

If a wrecked stem keeps one family of its old lattice exactly, then the angle it settles at is not free. Over the period of the family that survived, the pattern has to come back to where that family left it — which means the whole change in the divergence is a whole number of turns spread over a small whole number of organs. Measured, it is one turn, at seventeen of nineteen.

 Where the angle comes from

Three organs and no mirror

A coarse stem cut of two organs can end up as its own mirror image — the same lattice wound the other way, counts unchanged, handedness reversed. Finer stems never do it, and two accounts of why were on the table: coarseness, or the share of the neighbourhood removed. A three-organ cut at the finer arrangements settles it, and the answer is the first.

 Where the angle comes from

The share was not the thing

Two organs out of a front of five reverses a stem's handedness; three out of eight does not, and neither does five out of eight, which is a larger share of a larger neighbourhood. The hypothesis under test was that the dose decides the destination. It decides whether a stem falls off its lattice and nothing about where it lands.

 Where the angle comes from

A wreck has a short list

Cuts of one organ through five, over two hundred and forty-six stems that never came back, land on six settled divergences between them. Removing five organs instead of one wrecks nearly everything and reaches nowhere the single cut had not already found — and half the list turns out to be the old lattice slipped by a turn, while the other half is not the old lattice at all.

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