NEW YORK — As a president, Herbert Hoover ranks near the bottom in the hearts of most historians, condemned as the dull-minded bureaucrat who looked on while the nation sank into the Great Depression.

But in at least one respect, Hoover’s sad, single term was not a waste of time. Surprisingly, he was apparently never more productive than when supposedly wasting his time, assembling what may be his supreme presidential legacy: A new book demonstrates that he was the nation’s foremost executive doodler.

“Presidential Doodles,” just released by Basic Books, a member of the Perseus Books Group, has collected the random sketches and drawings by many of the nation’s commanders in chief, including not only Hoover’s elaborate shapes and swirls but the isolated squiggles of Abraham Lincoln. The book expands upon an issue of Cabinet Magazine, a quarterly of “Arts & Culture” that featured the jottings of eight presidents.

“Just as our dreams and little Freudian slips can mean something about us, doodles can be indicative of the person and issues and things that he is dealing with,” Cabinet’s editor-in-chief, Sina Najafi, said. Personalities emerge at a glance: John Adams’s hard, straight lines and precise geometrical patterns; Theodore Roosevelt’s rugged sketch of two dogs staring across a campfire; Dwight Eisenhower’s plain, practical illustrations; Ronald Reagan’s childlike portraits, including of himself in a cowboy hat.

President Kennedy, known for separating his life into compartments, would enclose words and numbers inside circles and boxes. Events long after his death give one doodle an unintended chill: A small circle with the numbers “9–11” contained within. Just to the lower left on the page, the word “conspiracy” is underlined. In summer 1964, as the Vietnam War intensified, President Johnson scribbled “Breakdown” at the top of one paper. Richard Nixon left behind few doodles, but, characteristically, kept an eye on what his adversaries wrote down, once noticing that Soviet leader Leonid Brezhnev sketched a heart with an arrow through it as talks faltered on limiting nuclear warheads.

Hoover’s work is the subject of 16 pages, six more than the man who displaced him from office and, for the most part, from history: Franklin Delano Roosevelt. Trained as an engineer, Hoover sketched out designs that read like building projects gone awry or one’s own imprisoned thoughts — circles within circles and diamonds inside diamonds, dark spirals reminiscent of spider webs or of wheels turning madly.

Hoover was not the first executive doodler, but he was the first to become famous for it. In 1929, an autograph collector got his hands on some sketches, which inspired newspapers to publish a wave of articles and a dressmaker to use Hoover’s designs for a line of one-piece children’s garments.

“Doodling is a 20th-century form,” Mr. Najafi noted. “You had the rise of bureaucracy and meetings and the demise of the secretary who would take notes.”

Some presidents, and their legacy keepers, have been proud of their doodles. Kennedy’s scribbles were exhibited after his death and even turned into sculpture. Presidents Eisenhower and Reagan were both fond of showing off their drawings, although, a CBS report noted at the time, if Reagan drew a horse or football player in your presence, it meant you had committed a grave error; you bored him.