1986/07/01 by Enrico Bombieri, John E. Taylor · 108 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #semigroups and automata theory #Physics #Statistical physics
paper · doi:10.1051/jphyscol:1986303
published in Le Journal de Physique Colloques 47(C3), C3-19 (EDP Sciences)
openalex publication_date 1986/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
We report on a preliminary investigation of the connections between quasiperiodic tilings, algebraic number theory, and cut-and-project sets. We substantially answer the question "which 1-dimensional tilings obtained by inflation rules are quasiperiodic" by showing that in general the characteristic equation of the inflation rule should have one root of absolute value greater than one and the rest of absolute value less than one. We also show that the vertices of such a tiling are contained in a cut-and-project set.