Wolfram’s Classification and Computation in Cellular Automata Classes III and IV

  • Genaro J. Martínez
  • Juan C. Seck-Tuoh-Mora
  • Hector Zenil
Part of the Emergence, Complexity and Computation book series (ECC, volume 2)


We conduct a brief survey on Wolfram’s classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram’s classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing-completeness or may turn out to be “too hot” in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing universality.


cellular automata universality unconventional computing complexity gliders attractors Mean field theory information theory compressibility 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Genaro J. Martínez
    • 1
    • 2
  • Juan C. Seck-Tuoh-Mora
    • 3
  • Hector Zenil
    • 4
  1. 1.Unconventional Computing Center, Bristol Institute of TechnologyUniversity of the West of EnglandBristolUK
  2. 2.Departamento de Ciencias e Ingeniería de la ComputaciónEscuela Superior de Cómputo, Instituto Politécnico NacionalMéxicoMéxico
  3. 3.Área Académica de IngenieríaUniversidad Autónoma del Estado de HidalgoPachucaMéxico
  4. 4.Behavioural and Evolutionary Theory Lab Department of Computer ScienceUniversity of SheffieldSheffieldUK

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