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- W1479901990 abstract "This is a chapter surveying the current state of our understanding of tilings with infinite local complexity. Such tilings can arise when tiles have infinitely many possible adjacencies, infinitely many shapes, or infinitely many labels. Our main requirement is that the set of tiles used to construct tilings should be compact. We consider tilings constructed in a number of ways, including the hierarchical methods of self-similarity, substitution, and fusion. We show how to adapt the standard toolbox for tilings with finite local complexity and suggest definitions for the concepts of fault lines and complexity functions. Three examples with infinite local complexity of distinctly different origin are fully analyzed using the tools and techniques contained in this chapter. We conclude with some important classes of open questions about tiling spaces with infinite local complexity." @default.
- W1479901990 created "2016-06-24" @default.
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- W1479901990 date "2015-01-01" @default.
- W1479901990 modified "2023-09-26" @default.
- W1479901990 title "Tilings with Infinite Local Complexity" @default.
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- W1479901990 doi "https://doi.org/10.1007/978-3-0348-0903-0_7" @default.
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