The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on communication complexity theory and, as a by-product, we provide (yet another) classification of cellular automata.
@article{arxiv.cs/0210008,
title = {Cellular automata and communication complexity},
author = {Christoph Durr and Ivan Rapaport and Guillaume Theyssier},
journal= {arXiv preprint arXiv:cs/0210008},
year = {2009}
}