Abstract
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.
Supported by the National Science Foundation under Grant No. CCR-9202396
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© 1994 Springer-Verlag Berlin Heidelberg
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Culik, K., Kari, J. (1994). Parallel pattern generation with one-way communications. In: Karhumäki, J., Maurer, H., Rozenberg, G. (eds) Results and Trends in Theoretical Computer Science. Lecture Notes in Computer Science, vol 812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58131-6_39
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DOI: https://doi.org/10.1007/3-540-58131-6_39
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