One key, decayed and windowed, through bursts and silence

One key, decayed and windowed, through bursts and silence

The blue curve is an exponentially decayed counter with a half-life of 4 s. The second curve is an exact count over a window of 5.77 s — the window chosen so that the two agree in the mean on a steady stream. They do not agree here and the shape of the disagreement is the point: the windowed count is a step function that drops the moment an arrival leaves, and the decayed value is smooth and never reaches zero. Through a silence the window empties and the counter fades; through a burst the window jumps and the counter climbs behind it. Neither is wrong. They are answers to different questions, and a dashboard showing one labelled as the other is the ordinary case.

Drawn at 700 × 366, wide on the page. Everything above is what decay-curve returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

10 essays call decay-curve. 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.