They’re a diverse bunch — farmers and philosophers, scientists and a singer-songwriter — and Ms. Taylor, a former actress who first became involved with the group in the early 1990s, uses her familiarity to encourage them to open up. Merging homey interviews with photographs and film of the hundreds of varieties of patterns (which pop up mysteriously overnight and are found all over the world), the film makes no pretense of objectivity or analysis. Everyone on screen — most sporting little blue flowers in their lapels, like a club insignia — is convinced of an intelligence behind the designs.

“I knew that something beyond the beyond was going on,” one interviewee says, echoing the metaphysical beliefs of many circle fans. But it’s the film’s geometrists who enthrall most, revealing that many of the shapes — one of which famously made the cover of a 1990 Led Zeppelin album — hold entirely new answers to Euclidean problems.

Set mainly in the bucolic beauty of Wiltshire, England (a hotbed of circle activity), “What on Earth?” touches on famous hoaxes and enjoys a brief visit to the conspiracy-theory place.

The film’s main attractions, though, are the patterns themselves: fantastically precise whorls and curlicues, radiolaria and mandalas that drift across the screen like the endlessly reforming crystals in a kaleidoscope. Whether designed by nature or by little green men, they make you want to believe.

WHAT ON EARTH?

Opens on Friday in Manhattan.

Produced and directed by Suzanne Taylor, edited by Mary Duprey; music by Bruce Hanifan; released by Mighty Companions. At the Quad Cinema, 34 West 13th Street, Greenwich Village. Running time: 1 hour 21 minutes. This film is not rated.