Planar Trivalent Network Computation

  • Tommaso Bolognesi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4664)


Confluent rewrite systems for giant trivalent networks have been investigated by S. Wolfram as possible models of space and spacetime, in the ambitious search for the most fundamental, computational laws of physics. We restrict here to planar trivalent nets, which are shown to support Turing-complete computations, and take an even more radical, approach: while operating on network duals, we use just one elementary rewrite rule and drive its application by a simple, fully deterministic algorithm, rather than by pattern-matching. We devise effective visual indicators for exploring the complexity of computations with elementary initial conditions, consisting of thousands of graphs, and expose a rich variety of behaviors, from regular to random-like. Among their features we study, in particular, the dimensionality of the emergent space.


Digital physics trivalent network complexity indicator  cellular automata two-dimensional Turing machine turmite emergent space 


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  1. 1.
    Zuse, K.: Rechnender raum. Elektronische Datenverarbeitung 8, 336–344 (1967)Google Scholar
  2. 2.
    Zuse, K.: Calculating space (rechnender raum), Tech. rep., MIT, Cambridge, Mass., technical Translation AZT-70-164-GEMIT (1970)Google Scholar
  3. 3.
    Wolfram, S.: A New Kind of Science. Wolfram Media, Inc. (2002)Google Scholar
  4. 4.
    Cook, M.: Universality in elementary cellular automata. Complex Systems 15(1), 1–40 (2004)MathSciNetGoogle Scholar
  5. 5.
    Smolin, L.: Atoms of space and time. Scientific American, 56–65 (2004)Google Scholar
  6. 6.
    Bolognesi, T.: Planar trivalent network computation, Tech. rep., CNR-ISTI, Pisa, 2006-TR-41 (December 2006)Google Scholar
  7. 7.
    Bolognesi, T.: Behavioural complexity indicators for process algebra: the NKS approach. Journal of Logic and Algebraic Programming (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tommaso Bolognesi
    • 1
  1. 1.CNR-ISTI, Istituto di Scienza e Tecnologie dell’Informazione ”A. Faedo”, 56124, PisaItaly

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