Generator

branch-stems

The top 70 organs of two stems grown by the same placement rule at the same rise of 0.013, differing only in the stretch of ideal lattice each was started from. The left one was seeded at the golden angle and settles at 136.781° with the pair 5/8; the right one was seeded on the Lucas lattice and settles at 99.785° with 4/7. Neither drifts towards the other: 0.73° and 0.28° from where each was seeded, over four hundred organs. That is what makes an intervention on the right-hand stem a measurement about a different lattice rather than about a different rule — and 4 and 7 are not Fibonacci numbers, which is the property the experiment needs.
One rule, one rise, two branches that stay where they were putThe top 70 organs of two stems grown by the same placement rule at the same rise of 0.013, differing only in the stretch of ideal lattice each was started from. The left one was seeded at the golden angle and settles at 136.781° with the pair 5/8; the right one was seeded on the Lucas lattice and settles at 99.785° with 4/7. Neither drifts towards the other: 0.73° and 0.28° from where each was seeded, over four hundred organs. That is what makes an intervention on the right-hand stem a measurement about a different lattice rather than about a different rule — and 4 and 7 are not Fibonacci numbers, which is the property the experiment needs.golden136.781° · 5/8Lucas99.785° · 4/7seeded at 137.51° and 99.50°, then left to the rulerise 0.013 · scatter 0.239° and 0.101°generated from a stated rule, not drawn to look right

Drawn at its defaults, in what the wrecked orbit inherits. 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

Stems and cones

The forks are exact

Where a stem's pattern has to choose between two futures, three spiral families are equally short and the lattice is exactly equilateral. A numerical solver found those points; the numbers it returned turned out to be rational, and chasing that gave a closed form — including the fact that every fork sits at a rational divergence, and the golden angle at none of them.

Stems and cones

Two accounts of one number

A stem that never recovers from an ablation settles into a repeating block whose length was the smaller of its two spiral counts, at both arrangements it had been measured at. Two different explanations predicted exactly that and could not be told apart. Swept across four rises on the ordinary branch the premise itself fails: at one arrangement the block is the larger number, at another both appear, and the rule that seemed to be there was two measurements.

The claims, measured

Matching instead of correcting

Two rounds of work failed on one question because every instrument's free parameter was set by the thing under test. The repair was not a better instrument or a model of the bias: it was choosing what to compare so that the confound could not vary. That move is available in four other places here, and three of them have already used it without anybody naming it.

Stems and cones

A stem on the other branch

Every arrangement this collection had cut an organ out of carried Fibonacci counts, which is why two rival explanations of the block a wrecked stem settles into had never disagreed. A stem seeded on the Lucas lattice carries four and seven at the same rise, under the same rule. Cut, it settles on seven — the larger number, and not a Fibonacci one.

Where the angle comes from

The block is the count it was cut from

A stem that never recovers from an ablation settles into a repeating block of eight angles precessing by 22.7°. Eight was also the smaller parastichy number of the lattice that was cut, which left two possibilities and no way to choose between them. Cut a stem one rung coarser and the block is five.

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