Canonical Substitution Tilings of Ammann-Beenker Type

Introduces a large class of parallelogram tilings sharing two key features with the Ammann-Beenker tiling: construction by canonical projection from ℝ⁴ to the plane, and the admission of substitution rules. The paper characterises all tilings in this class and determines their substitution rules — showing in particular that each such tiling admits a countably infinite family of inequivalent substitution rules.

2004-01-01

Authors: E. O. Harriss, J. S. W. Lamb
Published in: Theoretical Computer Science, 2004
Links: DOI

BibTeX

@article{canonical-substitution-tilings,
  title   = {Canonical Substitution Tilings of Ammann-Beenker Type},
  author  = {E. O. Harriss and J. S. W. Lamb},
  journal = {Theoretical Computer Science},
  year    = {2004},
  volume  = {319},
  number  = {1-3},
  pages   = {241--279},
  doi     = {10.1016/j.tcs.2004.02.014},
}