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Computational irreducibility and the predictability of complex physical systems.

Navot Israeli1, Nigel Goldenfeld

  • 1Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080, USA.

Physical Review Letters
|March 5, 2004
PubMed
Summary

We demonstrate coarse-graining for all Wolfram

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Area of Science:

  • Complex Systems
  • Computational Theory

Background:

  • Cellular automata (CA) are models of computation.
  • Wolfram's classification categorizes CA behavior.
  • Computational irreducibility describes systems resistant to prediction.

Purpose of the Study:

  • To develop a method for coarse-graining cellular automata.
  • To explore predictability in computationally irreducible systems.
  • To construct coarse-grained CA emulating large-scale behavior.

Main Methods:

  • Applying coarse-graining techniques to elementary cellular automata.
  • Analyzing CA across all Wolfram classes.
  • Constructing new CA models from coarse-grained rules.

Main Results:

  • Coarse-graining is feasible for all Wolfram CA classes.
  • Computationally irreducible systems can exhibit coarse-grained predictability.
  • New CA models replicate large-scale dynamics without fine details.

Conclusions:

  • Coarse-graining offers a simplified view of complex CA.
  • Predictability can emerge at macroscopic scales.
  • Irreducible systems can be effectively simplified through coarse-graining.

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