Phyllotaxis
the spirals are counted, not admired
Concept

Destination — where it appears

A divergence a run arrived at and then held, which is what the settling table records a stem as reaching. It is not where a refusing stem is: eleven runs whose reported endpoint lies within a degree of one are in an orbit tens of degrees wide whose mean happens to land there.

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

All 19 destinations, counted at 17 windows from 20 to 800 organs. One row per destination, one cell per counting window, coarsest on the left. A dark cell is a window returning the same pair as the standing 200; a warm cell is a window returning a different one; a pale cell is a window that reaches below the run's own settling organ and was dropped. 5 of the 19 rows differ anywhere, and every difference sits left of the floor its own pair sets — 20 organs for a pair under 14 parastichies and the larger count plus 6 above it. The census read at 25 organs and at 800 is the same census.

The window nobody varied

Every parastichy pair this collection reports about the settling table was counted over the top two hundred organs of a run, and that number had never been moved. Moved seventeen ways across a factor of forty, on all three hundred and eighty-four settled runs, it changes nothing at all.

lattices · Read window The five readings of 384 whose two counted families wind the same way. Each row is an additive sequence with the term the counter stepped over drawn open between the two it returned. 4/9 is 1, 4, 5, 9, 14 with 5 skipped, and the pair a crossing requirement would have returned is 4/5 — a sequence the same destination's other runs already sit on. Dropping these readings takes the census at 40 starting angles from 31 arrangements and 15 sequences to 28 and 12, on 5 of 384 runs.

A sequence that was a reading

One of the settling table's additive sequences rested on a single count that skipped a term, and the account of it was that the count had been taken over the wrong patch. It was not. The counter works out whether its two families wind opposite ways and the reading throws the answer away, on five runs in three hundred and eighty-four.

lattices · Read window Predicted 29 of 63 settle; 17 do. The 63 wrecked runs of the slot design regrown to 1200 organs and put to the settling table's own criterion, unchanged in every tolerance. Rows are whether the 300-organ endpoint sat within 1 degree of a destination; columns are whether the regrown run settles. The prediction written down before the sweep was that the 29 agreeing runs would settle: 12 of them do and 17 refuse, and the whole set settles 17 rather than 29. Agreement carries information without being a rule — 41.4 per cent of the agreeing runs settle against 14.7 per cent of the others, an odds ratio of 4.09 and a phi coefficient of 0.300 — so an agreeing run is still likelier to refuse than to settle.

A destination or a refusal

Sixty-three wrecked runs were regrown to twelve hundred organs and put to the settling table's own criterion, unchanged in every tolerance. The prediction written down before the sweep said twenty-nine would settle; seventeen do, and the prediction is wrong on its own side of the table as well as in its total.

mechanism · Settling The same verdict at every length from 300 organs to 1200. The settling criterion applied to the first 300, 400, 600, 800, 1000, 1200 organs of each of the 63 regrown runs. It accepts 17 at every one of them and refuses 46 at every one, and not one run changes sides. A truncated twelve-hundred-organ run is the shorter run organ for organ, so this is a comparison of lengths rather than of growths. The slowest arrival in the whole set is 138 organs, so 140 is the measured requirement and 300 carries a factor of 2.1. The column drawn dark is 300 organs, where the verdict is 17 settled and 46 refused.

What a run length was hiding

The settling criterion returns an identical verdict on all sixty-three wrecked runs at every length from three hundred organs to twelve hundred, so run length explains nothing. What the sweep does find is that an endpoint is a mean over an orbit, and thirty-four refusers never come within a degree of their own reported endpoint.

mechanism · Settling

Named alongside it

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

Claim testingHonest limitsSettlingAttractorNegative resultCensusCensus designEndpointParastichy pairReading windowSettling criterionSummary statistic

All concepts