Phyllotaxis
the spirals are counted, not admired
Generator

hard-cut-has-steps

One height of an ideal lattice, swept around the circle. The exponential cut-off hands the rule a smooth landscape; the hard one hands it a landscape with steps, because a neighbour enters the sum as the candidate slides past it. Halving the sample resolution multiplies the largest jump between neighbouring points by 2.00 on the smooth curve and by 1.04 on the hard one — which is the definition of the difference, since a smooth function's steepest step is bounded by its derivative and a discontinuity's is not. An argmin taken over steps is pinned to the steps.
The landscape the rule chooses over, at a cut-off of 3 spacingsOne height of an ideal lattice, swept around the circle. The exponential cut-off hands the rule a smooth landscape; the hard one hands it a landscape with steps, because a neighbour enters the sum as the candidate slides past it. Halving the sample resolution multiplies the largest jump between neighbouring points by 2.00 on the smooth curve and by 1.04 on the hard one — which is the definition of the difference, since a smooth function's steepest step is bounded by its derivative and a discontinuity's is not. An argmin taken over steps is pinned to the steps.00.2500.5000.750100.2000.4000.6000.8001candidate azimuth, in turnsenergy the rule minimises, scaled to its own rangeexponentialhard — a step, not a sloperise 0.02 · p = 1two cut-offs, one lattice

Drawn at its defaults, in a neighbourhood written down as a claim. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 2 essays

the blast radius of changing it

Where the angle comes from

A neighbourhood is a hypothesis

Every simulation of this kind stops summing somewhere. The previous phase found that where it stops decides what pattern comes out — so the stopping place is not a detail of the program but a claim about how far a primordium's influence reaches, and it should be written down as one.

 Where the angle comes from

A hard edge is not a falloff

The prediction was that cutting the neighbourhood at three spacings would reproduce the pattern truncation had manufactured. It does — if the cut is smooth. A hard cut at the same distance produces no pattern at any width, and the reason is that it is the only one of the three whose neighbour set depends on where the candidate is.

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