Park Chan-wook, one of South Korea's best directors, gets lots of attention when he introduces a new movie. About 100 reporters showed up Monday morning for a screening of his latest work, a 30-minute short called "Paranmanjang," which is Korean for "Ups and Downs."

Some were there because of the way Mr. Park made the movie: shooting it entirely on the latest version of Apple Inc.'s iPhone.

"From...