Phyllotaxis
the spirals are counted, not admired
Generator

hop-spectrum

How much each lattice hop moves from organ to organ in a stem that never repaired after a single removal, over its last 120 organs. The lag-one hop is the divergence itself and it swings by 60 degrees. The lag-8 hop swings by 0.09 degrees and sits 0.19 degrees from where the undisturbed stem put it, so that one family of the original lattice is still standing organ by organ. Its multiples inherit the same steadiness and nothing else comes within a factor of twenty. The block of angles this stem repeats has a period of 8, which is the surviving lag and not a coincidence.
One wrecked stem, lag by lag — golden, rise 0.005, organ 4 backHow much each lattice hop moves from organ to organ in a stem that never repaired after a single removal, over its last 120 organs. The lag-one hop is the divergence itself and it swings by 60 degrees. The lag-8 hop swings by 0.09 degrees and sits 0.19 degrees from where the undisturbed stem put it, so that one family of the original lattice is still standing organ by organ. Its multiples inherit the same steadiness and nothing else comes within a factor of twenty. The block of angles this stem repeats has a period of 8, which is the surviving lag and not a coincidence.0°30°60°90°12345678910111213141516lag, in organshow much that hop moves (°)lag 8: 0.09°golden, rise 0.005 · organ 4 back · block 8the surviving lag is 8

Drawn at its defaults, in the hop a cut leaves standing. It carries a slider over which, 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

The pattern itself

A period that is not a count

Eighteen wrecked stems settle into a block whose period is one of their own spiral counts, and one settles into a block of four on a lattice counted 8 and 13. The odd one is not noise. It is the case that shows what the rule is actually conserving, and it is the reason this thread is about lattice steps rather than about spirals.

 Where the angle comes from

The hop that survived

A stem that never repairs after an organ is removed settles into an exactly repeating block of angles, and the period of that block is a spiral count of the lattice it was cut from. Nobody could say why. Read the wrecked stem by lags rather than by neighbours and the answer is one line: one family of the original lattice is still standing, organ by organ, and the block is its period.

 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.

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