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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2001: STACS 2001 pp 259–270Cite as

Generalized Langton’s Ant: Dynamical Behavior and Complexity

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

Abstract

Langton’s ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general pla- nar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the square and the hexag- onal grids, we associate a P-hard problem to the dynamics. Finally, we show strong spatial restrictions on the trajectory of the ant in infinite bi-regular graphs with degrees strictly greater than 4, which contrasts with the high unpredictability on the graphs of lower degrees.

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Author information

Authors and Affiliations

  1. Center for Mathematical Modeling and Departamento de Ingeniería Matemática, FCFM, U. de Chile, Casilla 170/3-Correo 3, Santiago, Chile

    Anahí Gajardo, Eric Goles & Andrés Moreira

  2. Laboratoire de l’Informatique du Parallélisme, ENS-Lyon, 46, allée d’Italie, 69364, Lyon, France

    Anahí Gajardo

Authors
  1. Anahí Gajardo
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  2. Eric Goles
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  3. Andrés Moreira
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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Gajardo, A., Goles, E., Moreira, A. (2001). Generalized Langton’s Ant: Dynamical Behavior and Complexity. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_23

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  • DOI: https://doi.org/10.1007/3-540-44693-1_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

  • eBook Packages: Springer Book Archive

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