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sample-against-a-sweep

Above, offset 8's answer at every rise of the band. Below, the same row with only the rises a 9-cut design visits, which is one every 16. The design was built for a quantity expected to be constant and it reports the ends and the crossing correctly; what it cannot report is where inside the band the answer changes, or that it changes back. Every island here is 1 or 1 or 2 or 1 or 2 or 1 or 2 or 1 or 3 or 1 rises wide, against a step of 16, so the sample can only land on one by accident.

What nine rises could see of 126. Above, offset 8's answer at every rise of the band. Below, the same row with only the rises a 9-cut design visits, which is one every 16. The design was built for a quantity expected to be constant and it reports the ends and the crossing correctly; what it cannot report is where inside the band the answer changes, or that it changes back. Every island here is 1 or 1 or 2 or 1 or 2 or 1 or 2 or 1 or 3 or 1 rises wide, against a step of 16, so the sample can only land on one by accident.

Drawn at its defaults, in one band, cut at every rise. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 4 essays

the blast radius of changing it

Stems and cones

Every rise of a band

A band is cut at nine rises because the quantity it was built to test is a constant, and a constant is checked at the ends and at the crossing. On the widest band that quantity turned out not to be constant, which makes nine the wrong number. This is all hundred and twenty-six.

Stems and cones

The alternation is not a period

Nine sampled rises gave 8, 4, 8, 4 at one offset of one band, and a period was the obvious thing to look for. At full resolution it is thirteen islands one to three rises wide, with gaps of 1, 2, 3, 6, 7, 8, 9, 16, 31, 44 and 48 — and a fitted period buys exactly nothing.

Stems and cones

Three offsets, three crossings

The claim the band design rests on is that the survivor does not change where the two contact steps change places. It holds at full resolution: nineteen changes and not one at the handover. Where they are is three different rises, eight, nineteen and twenty-nine below it.

Stems and cones

The offsets that never change

Three of the six offsets that wreck anywhere on the band keep the same family at every rise they wreck at — 98, 22 and 81 rises of the 126. And which offsets wreck at all is a function of the rise, which no reading of a band had drawn.

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