The Rauzy Gasket
Pierre Arnoux, Štěpán Starosta · Birkhäuser Boston eBooks · 2013
We define the Rauzy gasket as a subset of the standard two-dimensional simplex associated with letter frequencies of ternary episturmian words. We prove that the Rauzy gasket is homeomorphic to the usual Sierpiński gasket (by a two-dimensional generalization of the Minkowski ? function) and to the Apollonian gasket (by a map which is smooth on the boundary of the simplex). We prove that it is also homothetic to the invariant set of the fully subtractive algorithm, hence of measure 0. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.