Generalized Β-expansions , Substitution Tilings , and Local Finiteness

@inproceedings{Robinson2005Generalized,
  title={Generalized Β-expansions , Substitution Tilings , and Local Finiteness},
  author={E. Arthur Robinson},
  year={2005}
}
For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion β is a Pisot number, then the tilings defined by the substitution must be locally finite. We also give a simple example of a two-dimensional substitution on rectangular tiles, with a non-Pisot length expansion β, such that no tiling admitted by the… CONTINUE READING