Phyllotaxis
the spirals are counted, not admired
Generator

The two shortest hops across the Lucas 7/11 rung, and where they cross

The lengths of the two shortest hops at every one of the 378 rises of the rung, fine on the left, computed from the settled divergence rather than measured off a cut. They cross exactly once, between 0.00804 and 0.00803, which is this rung's handover. The rise at which a cut first keeps the longer family is 164 steps of the grid further down and is marked separately; nothing happens to either length there.
The two shortest hops across the Lucas 7/11 rung, and where they cross. The lengths of the two shortest hops at every one of the 378 rises of the rung, fine on the left, computed from the settled divergence rather than measured off a cut. They cross exactly once, between 0.00804 and 0.00803, which is this rung's handover. The rise at which a cut first keeps the longer family is 164 steps of the grid further down and is marked separately; nothing happens to either length there.

Drawn at its defaults, in where the survivor changes on a rung. 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

Stems and cones

One step of the grid, again

A search of the fine end stepped from one rise to another a hundred grid steps away, and the family a cut keeps changed somewhere between. Cutting the rises in between puts the change inside one step, with the lattice identical on both sides.

 Stems and cones

The hops cross once

Walking a whole rung at the grid its rises are named on costs a few hundred stems and no cuts at all, and it answers a question nobody had asked: whether a rung has one handover or several. It has one, and the ladder had recorded it in the wrong place.

 Stems and cones

Two rises far apart

The whole handover thread rests on the claim that where the two contact steps change places is not where the survivor does. On one rung both rises are now located to a single step of the grid, and they sit forty-five per cent of the rung apart.

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