One cost follows the alphabet and the other follows the answer

One cost follows the alphabet and the other follows the answer

A 32-symbol alphabet throughout, with the measured stretch drawn from a restricted sub-alphabet so that the number of distinct symbols moves and sigma does not. The loop is flat at 320 ranks: it asks about every symbol whether or not the symbol is there. The descent rises from 10 to 62 — a factor of 32x down to 5.16x — and rises like d log(sigma/d) rather than like d, because the ancestors of few leaves overlap near the root and the ancestors of many do not. At d = sigma the walk enters every node and the two are within 5.16x, which is the two-ended shape of the claim.

Drawn at 700 × 420, wide on the page. Everything above is what interval-symbols returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

8 essays call interval-symbols. 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.