Phyllotaxis
the spirals are counted, not admired
Generator

same-scatter-different-noise

The amplitudes differ — field 0.0056 (fraction of the barrier), jostle 0.15 (degrees of azimuth), placement 0.18 (degrees of azimuth) — and are in different units, so they cannot be compared directly. What can be compared is what they produce, and matched here they are within 27% of one another. Everything a finished pattern records about its noise is shared between the three.
Three kinds of noise, matched at 0.75° of divergence scatterThe amplitudes differ — field 0.0056 (fraction of the barrier), jostle 0.15 (degrees of azimuth), placement 0.18 (degrees of azimuth) — and are in different units, so they cannot be compared directly. What can be compared is what they produce, and matched here they are within 27% of one another. Everything a finished pattern records about its noise is shared between the three.field — before the choice0.92°amplitude 0.0056jostle — before the choice0.70°amplitude 0.15placement — after it0.79°amplitude 0.183 runs each, at the amplitude that reaches 0.75°27% apart on the ruler

Drawn at its defaults, in noise that arrives through the neighbours. 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

What a plant might be doing

The noise that arrives through the neighbours

The two kinds of noise this site had were idealisations that bracket the rule's choice. The realistic disturbance is neither: a primordium is placed exactly, and then the organ grows, so by the time the next one forms its neighbours have moved. That is a third kind, and it is invisible in every measurement a plant offers.

 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.

 Stems and cones

What one angle says about the next

A tenth of a degree of placement noise moves a stem's divergence scatter from 0.50° to 0.62°, which nobody would report. It takes the correlation between consecutive angles from 0.54 to below zero. The other two kinds of noise, at scatters where no measurement can separate them, leave it at 0.6.

 Where the angle comes from

Which minimum was chosen

The rule takes an argmin, so there are two completely different things noise can do to it: move the answer, or move the question. One of them can change what is chosen and the other cannot, ever — and the difference is exactly zero against one or two placements in a thousand, at amplitudes where every other measurement says the two are identical.

 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