volume 29, issue 3, P459-467 2003
DOI: 10.1007/s00454-002-0758-3
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Abstract: Tilings of R 2 can display hierarchy similar to that seen in the limit sequences of substitutions. Self-similarity for tilings has been used as the standard generalization, but this viewpoint is limited because such tilings are analogous to limit points of constant-length substitutions. To generalize limit points of non-constant-length substitutions, we define hierarchy for infinite, labelled graphs, then extend this definition to tilings via their dual graphs. Examples of combinatorially substitutive tilings…

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