Conlon Nancarrow (1912-1997) turned to player pianos because they could reproduce complicated rhythms that were impossible for a human to play precisely. He also used different types of symmetry to compose pieces such as this canon. These symmetries are visually evident in the rolls themselves.
Steve Reich’s “Clapping Music” uses a single repeated rhythm pattern. The two players start by clapping the 12-beat pattern together in unison. After eight measures, one performer shifts the pattern forward by one beat and they clap the new pattern for eight measures. This process is continued until the two patterns align again. Here’s a visualization. Reich says that the piece was inspired by the clapping patterns in traditional flamenco music of the Roma people in Andalusia, Spain.