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On Canonical Substitution Tilings

My PhD Thesis with Jeroen Lamb, looking at the question of canonical projection method tilings which also have a substitution rule.

2004-01-01

Authors
Edmund Harriss
Published in
Imperial College London, 2004
BibTeX 
@phdthesis{canonical-substitution-tilings-phd,
  title   = {On Canonical Substitution Tilings},
  author  = {Edmund Harriss},
  school = {Imperial College London},
  year    = {2004},
}

The broad idea is that canonical projection tilings have substitution rules when the projection commutes with a hyperbolic automorphism of the lattice which acts as a scaling on the interior space.

The thesis also characterises all possible substitution rules for the Penrose and Ammann-Beenker tilings. The methods are constructive throughout.