In 1957, Walt Disney laid out what was then an astonishing plan for an entertainment ecosystem: Animated movies would fuel theme park attractions, which in turn would power merchandise sales, which would create interest in more movies. Today, with “Frozen,” the plan has evolved further.

When the movie became a blockbuster in 2013, taking in $1.3 billion globally, Disney got busy: It rushed out merchandise, sent Princesses Anna and Elsa on an ice-show tour and started work on an Arendelle boat ride at Epcot and three stage musicals.

Robert A. Iger, Disney’s chief executive, told a Wall Street conference last month that he had recently seen a “Frozen” show bound for Disney California Adventure. He noted that “Frozen” would be part of the parade at the new Shanghai Disneyland. And, he said, “I sat on Friday here in New York in a run-through of the ‘Frozen’ musical that we’re starting to develop for Broadway.”

It’s an increasingly familiar approach: Both “Beauty and the Beast” and “Aladdin” had theme park shows before New York productions. (Broadway veterans helped create them all.)