Phyllotaxis
the spirals are counted, not admired
Generator

a-finer-grid

Five stems at each of five disturbances, all at a rise of 0.0019, read through a lag window of 45 from a seed of 40 nodes. A filled mark is a stem that returned 13/21, which is what the position counter finds in it; an open mark is a refusal. The only difference between the two rows is how many azimuths the placement rule samples when it takes its minimum: 384, which every run on this site has used since the foundation phase, against 1152. At the coarse grid the rule locks onto its own sample points and the readout refuses 22 of 25 stems; at the fine one it reads all 25. The ceiling was a parameter of the program.
The 13/21 rung, at two azimuth gridsFive stems at each of five disturbances, all at a rise of 0.0019, read through a lag window of 45 from a seed of 40 nodes. A filled mark is a stem that returned 13/21, which is what the position counter finds in it; an open mark is a refusal. The only difference between the two rows is how many azimuths the placement rule samples when it takes its minimum: 384, which every run on this site has used since the foundation phase, against 1152. At the coarse grid the rule locks onto its own sample points and the readout refuses 22 of 25 stems; at the fine one it reads all 25. The ceiling was a parameter of the program.disturbance0.080.10.130.150.18384 azimuthsstep 0.94°1 of 25 read 13/21scatter 44.9°1152 azimuthsstep 0.31°25 of 25 read 13/21scatter 0.4°rise 0.0019 · seed 40 nodesgenerated from a stated rule, not drawn to look right

Drawn at its defaults, in the rung, the window and the sample grid. 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

Where the angle comes from

Where the model stops

Below a growth parameter of about 0.18 this implementation does not converge — the settled angle wanders over a hundred degrees however long the run. That is the range where the literature says the interesting behaviour lives, and it is worth a figure rather than a quietly chosen axis.

 Where the angle comes from

A window that makes a pattern

A rule whose energy has no well-defined minimum produces a clean 8/13 lattice at 137.62°, with half a degree of scatter, when its neighbourhood is cut at three node spacings. Let it see twelve and the pattern is gone. Every simulation of this kind truncates something, and truncation manufactures exactly the result it is used to look for.

 Stems and cones

Two readings from one stem

Three phase plans in a row have recorded that the two statistics of a divergence sequence want opposite plants — one quiet, one disturbed. Measured on the same stems they do not. The conflict was in the interpretation of a sign, and the window in which both are readable is wide.

 Stems and cones

The rung was not the instrument

The previous phase said the pair readout has a ceiling one rung above where it works, that this is arithmetic rather than statistics, and that no amount of stem fixes it. The arithmetic is right and gives a band of lag windows that is never empty; what was actually stopping the reading was an eight-node seed and a grid of 384 azimuths.

 Where the angle comes from

What a sample grid decides

The rule takes its minimum over 384 sampled azimuths, and that number has been a constant since this site's first commit. Tripling it changes nothing at the two rises the collection argues from — five runs of five, identical readings — and changes which answer appears at the one rise published as having no answer. A parameter of the program, measured rather than assumed.

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