There I was, riding the subway over the Williamsburg Bridge, making a dance. The stage was my iPad.

With a tap of a beige circle Daniel Ulbricht — wearing beige — feet planted wide, stood with his back to me. Turning to the right and then to the left as if trapped in a cage, he suddenly gave in to momentum and spun forward. Tapping a white circle caused another version of Mr. Ulbricht to appear in the background — in another dance. In a flash of synchronicity, both ticked their arms like clock hands before breaking the unison with a breezy sequence of steps that displayed two techniques all choreographers have in their toolbox: canon and retrograde.

Passe-Partout, the newest dance application by the 2wice Arts Foundation, is its most complex yet. Produced by Patsy Tarr and designed by Abbott Miller, this app presents a new stage for dance that allows a user to overlay a series of one-minute pieces onto one another — there are eight solos or duets in total, though only five can be seen simultaneously — choreographed by Justin Peck for Mr. Ulbricht and himself. These layers allow for more than 13,000 permutations of dances. That’s a lot of bang for 99 cents.

In the dances, Mr. Peck and Mr. Ulbricht, members of New York City Ballet, are accompanied by the music of Aaron Severini, a former City Ballet member turned composer, who focuses on different instrumentation for each piece he composed; even if more than one is playing, they don’t clash. He created for clarinet, piano, harp, harpsichord, marimba and percussion.

In this choreographic pursuit, there are no wrong choices. And unlike ballets for the stage, which disappear once the curtain falls, the dances made for Passe-Partout can be saved or shared through social media. Since one mission of 2wice is to educate the public about dance, Ms. Tarr, its effervescent, philanthropic president, wanted to tackle the rudiments of choreography.