One construction follows the text and the other follows its square

One construction follows the text and the other follows its square

The same parse, built two ways, over a collection growing from 512 to 8,192 characters. The quadratic construction compares characters: 7,906 at the small end and 1,324,336 at the large, which is 168x for 16x of text. The automaton follows transitions and walks suffix links: 1,659 to 25,420, which is 15x. The two units are different acts and the ratio between them is not a speed-up; what the plate shows is that one grows with the text and the other with its square. Both produced identical parses, phrase for phrase, at every size. Both axes are logarithmic.

Drawn at 700 × 430, wide on the page. Everything above is what automaton-parse 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 automaton-parse. 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.