Origami is the ancient Japanese art of paper folding. One uncut square of paper can, in the hands of an origami artist, be folded into a bird, a frog, a sailboat, or a Japanese samurai helmet beetle.

Origami, a more than 2,000-year-old traditional Japanese art form, is now considered by many as only a pastime for young children. But the new play “Animals Out of Paper” by Rajiv Joseph, which opened ...