3 papers
math.DS2026
Recognisability for generalised hierarchical pattern spaces of finite local complexity
James J. Walton
We develop a general framework of Euclidean patterns and pattern spaces of translational finite local complexity (FLC), analogues of translational tiling spaces. The notion of a se…
math.DS2025
When is a cut and project set substitutional?
Edmund Harriss, Henna Koivusalo, James J. Walton
Cut and project sets are obtained by projecting an irrational slice through a lattice to a lower dimensional subspace. Under standard conditions, the resulting pattern has no trans…
math.DS2025
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…