Phyllotaxis
the spirals are counted, not admired
Generator

noise-against-rate

Three stems from one initial condition. Halving the rate carries it from 7/11 to 8/13 with the divergence scatter under a degree in both. Holding the rate and adding the most noise a lattice survives leaves 0 per cent of runs on the branch they started on, and 67 per cent with no pattern at all.
The rate moves the branch; the noise only breaks the patternThree stems from one initial condition. Halving the rate carries it from 7/11 to 8/13 with the divergence scatter under a degree in both. Holding the rate and adding the most noise a lattice survives leaves 0 per cent of runs on the branch they started on, and 67 per cent with no pattern at all.what changedcounted at the topscatter65 nodes per rung, no noise7/110.64°131 nodes per rung, no noise8/130.69°65 per rung, noise at 0.0150% still Lucas12.65°a change of branch is a clean lattice on the other ladder,which the rate produces and the noise never doesseeded 40 nodes of Lucas lattice at a rise of 0.127/11 → 8/13 by rate alone

Drawn at its defaults, in noise, and where it gets in. 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

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.

 Where the angle comes from

Noise is not a slow rate

A stem seeded on the Lucas branch keeps it below ninety nodes per rung and abandons it above — which invites the objection that a real apex's fluctuations would knock it off regardless. Measured across a hundred and sixty runs of two independent kinds of noise, one escapes, at the amplitude where the pattern is already coming apart.

 Where the angle comes from

The boundary belongs to the pattern

Three kinds of noise, in three incommensurable units, destroy a lattice at the same place — about a degree and a half of divergence scatter. The previous phase measured that of two kinds and called it a scale rather than a constant. With a third it looks less like a coincidence and more like a property of what a lattice is.

All 105 generators