An interesting paper of interest to our readers just came out from another set of researchers interested in higher dimensional complexity. It shows why native 2D measures are interesting and needed. "Complexity of Two-Dimensional Patterns" http://arxiv.org/pdf/cond-mat/9804071.pdf With a generalization of regular language for 2D patterns and time complexity results. Further research should be done for more powerful languages. Enjoy.

Hector Zenil