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- W3048347961 abstract "A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system (GIFS), based on a combinatorial structure we call a pre-tree, is introduced. For each GIFS, a family of tilings is constructed indexed by a parameter. For what we call a commensurate GIFS, our method is used to define what we refer to as balanced tilings. Under mild conditions on the commensurate GIFS and the parameter, the resulting balanced tilings have a finite set of prototiles, are self-similar, and are quasiperiodic. A notion of rigidity is defined for a commensurate GIFS, and a necessary and sufficient condition for two rigid balanced tilings to be congruent is provided. For a given rigid GIFS, there are uncountably many balanced tilings, corresponding to uncountably many parameters. All rigid balanced tilings are non-periodic." @default.
- W3048347961 created "2020-08-13" @default.
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- W3048347961 date "2020-08-09" @default.
- W3048347961 modified "2023-09-24" @default.
- W3048347961 title "Tilings from graph directed iterated function systems" @default.
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- W3048347961 doi "https://doi.org/10.1007/s10711-020-00560-4" @default.
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