21 citations · 70 across the 14 of their papers we have counts for
16 papers
Rauzy fractals of random substitutions
Philipp Gohlke, Andrew Mitchell, Dan Rust +1
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a…
Corner the Empress
Robbert Fokkink, Gerard Francis Ortega, Dan Rust
Wythoff Nim aka Corner the Lady is a classic combinatorial game. A Queen is placed on an infinite chess board and two players take alternate turns, moving the Queen closer to the c…
Substitutions on compact alphabets
Neil Mañibo, Dan Rust, James J. Walton
We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important fea…
Automorphism groups of random substitution subshifts
Robbert Fokkink, Dan Rust, Ville Salo
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the a…
Spectral properties of substitutions on compact alphabets
Neil Mañibo, Dan Rust, James J. Walton
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows on…
Measure theoretic entropy of random substitution subshifts
Philipp Gohlke, Andrew Mitchell, Dan Rust +1
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking feat…