Parallel pattern generation with one-way communications

  • Karel CulikII
  • Jarkko Kari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 812)


We study (static) patterns generated by Cellular Automata (CA). In particular, we consider CA with one-dimensional information flow (for each axis of coordinates) called one-way CA and CA with information flow only away from the center of coordinates, called one-way rooted CA. For example, we show that any pattern that can be generated by a one-way CA can be generated in linear time. The converse holds in the one-dimensional case. We show an interesting connection between patterns generated by CA, fixed points of CA and tilings of Euclidean spaces. We show that it is undecidable whether a CA converges to a pattern from a given finite configuration or from any configuration.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Karel CulikII
    • 1
  • Jarkko Kari
    • 2
  1. 1.Dept. of Computer ScienceUniversity of South CarolinaColumbia
  2. 2.Mathematics DepartmentUniversity of TurkuTurkuFinland

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