Parallel pattern generation with one-way communications
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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