text: Stochastic music Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Xenakis, who coined the term stochastic music. Specific examples of mathematics, statistics, and physics applied to music composition are the use of the statistical mechanics of gases in Pithoprakta, statistical distribution of points on a plane in Diamorphoses, minimal constraints in Achorripsis, the normal distribution in ST/10 and Atrées, Markov chains in Analogiques, game theory in Duel and Stratégie, group theory in Nomos Alpha (for Siegfried Palm), set theory in Herma and Eonta, and Brownian motion in N'Shima.
  Xenakis frequently used computers to produce his scores, such as the ST series including Morsima-Amorsima and Atrées, and founded CEMAMu.
  Film music
  Examples of extensive aleatoric writing can be found in small passages from John Williams' score for the film Images. Other film composers using this technique are Mark Snow (X-Files: Fight the Future), John Corigliano, and others. Snow used digital samples of acoustic instruments "to merge starkly electronic timbres with acoustically based sounds, an approach developed extensively in his much celebrated music for The X-Files (1993–2002, 2016–18). Over the course of the series, Snow's often ambient music dissolved distinctions between sound design and musical score."
  Howard Shore employed aleatoric composition in The Lord of the Rings: The Fellowship of the Ring during the Fellowship's encounter with the Watcher in the Water outside of the gates of Moria.