Guess how.

His first machine (1957) was "a set of crank and lever arrangements similar to the ubiquitous child's circle pattern drawing toy". Saul Bass "included a few short sequences, drawn upon hundreds of animation cells with the machine's stylus, for the title to Alfred Hitchcock's film Vertigo." But every cel had to be photographed in turn, and Whitney "soon saw the absurdity". His next machine came from war surplus, an anti-aircraft gun director: "a $33,000 device" he could buy "for less than $200". The trick: "holding the camera shutter open while the light itself completed one excursion for each frame." On his 1961 reel the word 1961 orbits on a widening circle until it becomes "a progressively less readable pattern". The reel's copyright line: Motion Graphics, Inc. And the story that the gun computer drew Vertigo? In his own account, Vertigo came from the first machine.

Our own machine drawings, spiral and type; no frames from Vertigo or from Whitney's films.

Which title sequence would you study frame by frame?

Sources: John Whitney, "Animation Mechanisms", American Cinematographer, Jan 1971 (reprinted in Digital Harmony, 1980); John Whitney, A.S.I.D. talk, 1962 (Film Culture 37); BAMPFA catalogue record for Catalog (1961); AFI Catalog, Vertigo (1958).
Sounds: our own, made in code (earshot, CC0).