A Novel Algorithm for Coarse-Graining of Cellular Automata

  • Krzysztof Magiera
  • Witold Dzwinel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8751)


The coarse-graining is an approximation procedure widely used for simplification of mathematical and numerical models of multiscale systems. It reduces superfluous – microscopic – degrees of freedom. Israeli and Goldenfeld demonstrated in [1,2] that the coarse-graining can be employed for elementary cellular automata (CA), producing interesting interdependences between them. However, extending their investigation on more complex CA rules appeared to be impossible due to the high computational complexity of the coarse-graining algorithm. We demonstrate here that this complexity can be substantially decreased. It allows for scrutinizing much broader class of cellular automata in terms of their coarse graining. By using our algorithm we found out that the ratio of the numbers of elementary CAs having coarse grained representation to “degenerate” – irreducible – cellular automata, strongly increases with increasing the “grain” size of the approximation procedure. This rises principal questions about the formal limits in modeling of realistic multiscale systems.


multiscale systems coarse graining cellular automata 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Krzysztof Magiera
    • 1
  • Witold Dzwinel
    • 1
  1. 1.AGH University of Science and Technology, Department of Computer ScienceKrakówPoland

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