This volume constitutes the thoroughly refereed proceedings of the 21st International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015, held in Turku, Finland, in June 2015. This volume contains 4 invited talks in full-paper length and 15 regular papers, which were carefully reviewed and selected from a total of 33 submissions. Topics of interest include, the following aspects and features of such systems: dynamical, topological, ergodic and algebraic aspects
  algorithmic and complexity issues
  emergent properties
  formal language processing aspects
  symbolic dynamics
  models of parallelism and distributed systems
  timing schemes
  phenomenological descriptions
  scientific modeling
  and practical applications.