Phyllotaxis
the spirals are counted, not admired
Generator

survivor-grid

A row for each of twelve lattices and a column for each offset an organ is removed at, with the lag whose hop survived written in the cell. 30 cells never repair. The lag left standing is one of the two contact families at 29 of them, and at 17 it is the second shortest step on the lattice rather than the shortest, which is what refuses the reading that a rule holds its nearest neighbours. The ringed cells are the five the offset rule gets wrong. Two lattices carry no cells at all because no single removal wrecks them.
Which lag survives, at every lattice and every offsetA row for each of twelve lattices and a column for each offset an organ is removed at, with the lag whose hop survived written in the cell. 30 cells never repair. The lag left standing is one of the two contact families at 29 of them, and at 17 it is the second shortest step on the lattice rather than the shortest, which is what refuses the reading that a rule holds its nearest neighbours. The ringed cells are the five the offset rule gets wrong. Two lattices carry no cells at all because no single removal wrecks them.12345678910organ removed, places back from the tipgolden, rise 0.032··········Lucas, rise 0.026··········golden, rise 0.026···5······golden, rise 0.020···5······golden, rise 0.016···5······golden, rise 0.013···55·····golden, rise 0.010···55888··golden, rise 0.008···5588···golden, rise 0.005···8·4888·Lucas, rise 0.020···44·····Lucas, rise 0.013··74777···Lucas, rise 0.008····7777··shaded: the survivor is the second-shortest step — 17 of 30twelve lattices · 30 offsets that never repairgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in which hop the rule keeps. 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

A survivor has to be a neighbour

A stem that never repairs after a removal keeps exactly one lattice hop rigid, and nothing predicted which one. Sweep every offset at twelve lattices and the answer narrows sharply: at twenty-nine of thirty the surviving hop is one of the two families a counter returns, and the one exception is a step six times too long to be one.

 Where the angle comes from

Not the shorter of the two

If a damaged stem keeps one contact family standing, the obvious guess is that it keeps the nearer one. Across thirty wrecked offsets that is true twelve times and false seventeen, and on one lattice the two steps differ by a quarter of a per cent — where the words shorter and longer are doing no work at all.

 Where the angle comes from

One offset, two answers

Which contact family a wrecked stem keeps is decided by where the cut landed, at twenty-five of thirty offsets, by the simplest rule anybody would write down. It is refuted by two runs: the same counted pair, the same offset, two different rises, and two different surviving families.

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