Phyllotaxis
the spirals are counted, not admired
Concept

Instrument setting — where it appears

A number chosen when a measurement was designed rather than measured by it, such as a run length, a reading window or a sampling step. Three of them stand between the ablation census and every claim it makes, and each of the three has turned out to decide an answer.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

Each cut's class spread at three reading windows. The worst spread within a residue class, measured over the last 60, 120 and 180 organs of the same runs. A quantity that is steady with noise on it would give a flat line; a quantity drifting steadily along the run gives a line through the origin. Nearly every row gives the second, so the classes this thread calls steady are sliding slowly and the number that says how much depends on how much of the run is read. The dashed guide is exact proportionality.

A spread that grows with its window

A spread over a sample of a steady quantity does not depend on how big the sample is. These spreads triple when the window triples, on nearly every row of the census, which means the classes this thread calls steady are sliding — slowly, and invisibly at any single window.

mechanism · two windows Which cuts count as periodic, at each reading window. One row per wrecked cut and one column per window. A filled cell is a cut whose worst class spread is under the ten-degree line and is therefore called periodic. At 60 organs 28 of the 30 cuts are, at 120 organs 25, and at 180 organs 25. three rows change side, all of them losing their periodicity as the window widens, and they are marked.

The window nobody moved

Three instrument settings sit between the ablation census and every statement it makes. Two have been varied and both decided answers. The third is a hundred and twenty organs at the top of a run, it has never been moved, and moving it changes the verdict on three rows.

mechanism · two windows Where each window begins, against where the pattern begins. The run is drawn left to right, one bar per cut. The pale stretch is the disturbance still healing, up to the organ from which the profile holds its levels for the rest of the run; the dark stretch is the pattern repeating. The marks are the organ each of the three windows starts at, since a window is the last N organs of a run. On these rows the widest window starts inside the pale stretch, so it is reading the healing and calling it the pattern — which is why widening the window takes them off the periodic list.

Three rows a window moves

Three of the census's thirty cuts are periodic when a hundred and twenty organs are read and not when a hundred and eighty are. Their spreads do not grow in proportion to the window, they grow by twenty and forty times, and the reason is that a window is the tail of a run.

mechanism · two windows Where the doubled cut's run finishes, at every rise of the sweep. The divergence the wrecked run ends at, rise by rise. It takes only a handful of values and jumps between them at rises one part in a thousand apart, 4 times inside the 9 rises of the finest sweep alone — where the walls, the block, the intact stem's divergence and the rigid lags are all held. So the end of a wrecked run is not a stable quantity on this rung, and no statement about where the stem finishes is available on either side of the transition. The first organ's displacement is the reproducible half of the same measurement.

The end of a wrecked run

The obvious follow-up to a transition in where one organ goes is whether the stem also finishes somewhere different. On this rung the question has no answer: a wrecked run's final divergence takes four values and changes between rises a thousandth apart, three times inside a nine-rise sweep.

cylinder · both walls

Named alongside it

The objects these essays reach for when they reach for this one.

Claim testingHonest limitsArtefactDamage profileMeasurement errorPeriodicityReading windowResidue classAblationOnsetTransientBoth walls

All concepts