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Upper Bound on the Products of Particle Interactions in Cellular Automata

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  • Wim Hordijk
  • Cosma Rohilla Shalizi
  • James P. Crutchfield
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    Abstract

    Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles -- a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby eludicating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight. PACS: 45.70.Qj, 05.45, 05.65+b

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 00-09-052.

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    Date of creation: Sep 2000
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    Handle: RePEc:wop:safiwp:00-09-052

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