Recursion depth on already sorted input, against a stack of 512 frames

Recursion depth on already sorted input, against a stack of 512 frames

Stack frames held at the deepest point, on logarithmic axes, with a stated stack drawn across. Quicksort with a first-element pivot recurses once per element on this input and crosses the line; the other rules stay logarithmic and never approach it. The algorithm that crosses is the one universally described as sorting in place. The stack is a stated model, because a real one runs out at a size that depends on the engine and is not reproducible between runs.

Drawn at 690 × 410, wide on the page. Everything above is what stack-depth 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 stack-depth. 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.