An exponential histogram over a window of 400: 29 buckets, 200 against 200

An exponential histogram over a window of 400: 29 buckets, 200 against 200

Each box is one bucket: its label is how many ones it covers, always a power of two, and its position is the span of arrivals it summarises. At most 6 buckets of any one size are allowed, and the 1,764 merges so far are what has kept that true. The estimate counts every bucket in full except the oldest, which is counted half — the shaded one, which straddles the edge of the window with part of it already outside and nothing recorded to say how much. That single bucket is the entire error of the structure: here it is 32 of 215, so the estimate is out by at most 16 against a true 200, and it is out by 1. The structure holds 406 bits against the 400 the window itself would take.

Drawn at 700 × 178, wide on the page. Everything above is what window-buckets returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

4 essays call window-buckets. 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.