One tug-of-war register: 32 keys, each pulled one way or the other

One tug-of-war register: 32 keys, each pulled one way or the other

Every bar is one key of the stream, its height its exact count and its direction the ±1 the hash family drew for it. The register holds the sum, which is 9,034; the estimate is that number squared, 81,613,156, against a true F2 of 36,931,352 — 121.0% out on this draw. The bars very nearly cancel, and that is the mechanism rather than an accident: the cross terms cancel in expectation and what survives is the sum of the squares. Model: cash register, 20,000 updates.

Drawn at 700 × 224, wide on the page. Everything above is what tug-of-war-run returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

7 essays call tug-of-war-run. 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.