Phyllotaxis
the spirals are counted, not admired
Generator

growing-stem

365 nodes, each placed where the repulsion from the ones below it was least, with the rise falling from 0.2 to 0.0045. Counted blind in a sliding window the pattern walks 1/2 → 2/3 → 3/5 → 5/8 → 8/13, and the marks are where its answer changed.
A stem grown at 92 nodes per rung365 nodes, each placed where the repulsion from the ones below it was least, with the rise falling from 0.2 to 0.0045. Counted blind in a sliding window the pattern walks 1/2 → 2/3 → 3/5 → 5/8 → 8/13, and the marks are where its answer changed.1/2 at the bottom, 8/13 at the top342 nodes · rise 0.2 → 0.004587 nodes per rung

Drawn at its defaults, in the same pattern with a rate. It carries a slider over T, 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 3 essays

the blast radius of changing it

What a plant might be doing

A growing organ is part of the rule

Every model on this site places primordia on a surface and then treats the surface as furniture. But the surface grows between one placement and the next, and that growth reaches the rule through the only channel it has — where the neighbours are. What looks like a boundary condition turns out to be a term in the model.

 Where the angle comes from

A pattern with a rate

Every lattice on this site is a static object indexed by a parameter, and a plant is not. Put the rise on a clock, place each node where the repulsion from the ones below it is least, and the object that comes out has a history — which is the first thing here that could disagree with the ladder.

 Where the angle comes from

The rate decides the branch

Forty nodes of Lucas lattice, carried down to the same fine rise twice. Hurried, the pattern holds the Lucas ladder through three more forks at 99.5°. Given room, it abandons it at the first fork it reaches and walks to 8/13 at 137.5°. Same seed, same rise, two ladders — with a threshold between them at about ninety nodes per rung.

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