Surging demand caught Ms. Basford and her publisher off guard. Fan mail poured in from busy professionals and parents who confided to Ms. Basford that they found coloring in her books relaxing. More accolades flowed on social media, as people posted images from their coloring books.

Hard-core fans often buy several copies of her books at a time, to experiment with different color combinations. Others have turned it into a social activity. Rebekah Jean Duthie, who lives in Queensland, Australia, and works for the Australian Red Cross, says she regularly gathers with friends for “coloring circles” at cafes and in one another’s homes.

“Each page can transport you back to a gentler time of life,” she said of Ms. Basford’s books in an email.