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Abstract: In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that... (Update)
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...with two possible tilings carry truth values, and junctions in these wires simulate logical gates. Similar approaches are taken in [6, 9, 11 13]. The question of whether a tiling exists then corresponds to the canonical NP complete problem Satis ability, which asks whether a...
...are as many queens as rows and such that no queen strike another queen is a recognizable picture language. This example is inspired by [17] where the 8 queens problem is treated. For instance, with the alphabet Sigma = f ; g, the two following pictures are in this...
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BibTeX entry: (Update)
Lindgren, K., Moore, C., & Nordahl, M. (1997). Complexity of two-dimensional patterns. (Working Paper 97-03-023.) Santa Fe, NM: Santa Fe Institute. http://citeseer.ist.psu.edu/article/lindgren00complexity.html More
@techreport{ lindgren97complexity,
author = "K. Lindgren and C. Moore and M. Nordahl",
title = "Complexity of Two-Dimensional Patterns",
number = "97--03--023",
year = "1997",
url = "citeseer.ist.psu.edu/article/lindgren00complexity.html" }
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