Generator

bands-side-by-side

One row per band. Each runs from its coarse end on the left to its fine end on the right, with the rise at which the two contact steps change places marked, and the family that survives every wrecked cut written at the end. The 5/8 band on the golden branch keeps the 5 at all 24 of them and the 4/7 band on the Lucas branch keeps the 4 at all 31. Two branches, two counted pairs, one result: the quantity the band varies is not the quantity that decides the answer.

Both bands, on two branches and two pairs. One row per band. Each runs from its coarse end on the left to its fine end on the right, with the rise at which the two contact steps change places marked, and the family that survives every wrecked cut written at the end. The 5/8 band on the golden branch keeps the 5 at all 24 of them and the 4/7 band on the Lucas branch keeps the 4 at all 31. Two branches, two counted pairs, one result: the quantity the band varies is not the quantity that decides the answer.

Drawn at its defaults, in the band where two movers come apart. 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

Two lines that cross once

The divergence at which a lattice's two contact steps are exactly equal is a curve across each rung, computable from the geometry with nothing grown. The rule's own settled divergence is a second, shallower curve, and where they cross is where the step ordering changes hands.

Stems and cones

A band that holds the angle still

Around every handover the settled divergence has a shallow floor, so a run of rises either side of it share a divergence to a twentieth of a degree while their two contact steps change places. That is a matched pair with one quantity varying, and it is the design the ablation thread had no way to state.

Where the angle comes from

The side the census sat on

Eight of the ten lattices the ablation census wrecks at were grown past their rung's handover, one before it, and one so close that the ordering it quotes differs by parts in a thousand. A reading scored over the step ordering was therefore scored against a quantity the census was nearly holding fixed.

Where the angle comes from

The ordering was not the actor

Cut an organ out of every rise of a band where the counted pair and the settled divergence are held and the two contact steps change places, and the family left standing does not change. Fifty-five wrecked cuts on two branches, and the ordering reverses underneath every one of them.

Where the angle comes from

The organ that moved furthest

A reading that works on nine of thirty rows needs a reference organ, and the obvious repair is to measure one rather than to choose it. Measured, the disturbance turns out to have no far edge at all, so there is no organ that moved furthest in any sense the reading can use — and the generalisation that does work needs no reference organ.

All 207 generators