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Reinterpreting and Extending Anatol Vieru’s Periodic Sequences Through the Cellular Automata Formalisms

  • Paul LanthierEmail author
  • Corentin GuichaouaEmail author
  • Moreno AndreattaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

In this paper we focus on Anatol Vieru’s periodic sequences that we approach with the formalism of the theory of cellular automata. After extending previous results about the action (in the image direction) of one particular cellular automaton on periodic sequences we show the existence of a second one which is its complementary (or dual). The main idea of the paper is that the study of preimages of one of those two automata is the study of the images of the other one and vice versa. By using the duality, we have been able to show explicitly the evolution of the period and the form of the preimages for both automata. In order to illustrate the theoretical constructions, a musical composition is presented using the two automata both in the image and preimage directions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université de Rouen, LMRS (UMR 6085)Mont-Saint-AignanFrance
  2. 2.Université Strasbourg, USIAS/IRMA (UMR 7501)StrasbourgFrance
  3. 3.IRCAM/CNRS/Sorbonne UniversitéParisFrance

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