An ordered stream against its own shuffle, at every ratio of period to cycle

An ordered stream against its own shuffle, at every ratio of period to cycle

a ramp sweeping the whole range every p arrivals, run through a summary compressing every 50 updates, beside a random permutation of the identical multiset. The marked cycle lengths are the commensurate ones, where the compression instants fall at the same phase of the value cycle every time — which is the condition a block boundary aliases under. The commensurate cases depart from their controls 1.03 times as far as the incommensurate ones, against a sweep whose widest departure anywhere is 1.59. Nothing is happening at the marks.

Drawn at 700 × 372, wide on the page. Everything above is what schedule-aliasing returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

1 essay calls schedule-aliasing. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.