Grout: A 1-Dimensional Substitution Tiling Space Program

2015/12/01 by Scott Balchin, Balchin, Scott, D. M. Rust +1
Computer Science · Materials Science · #37B10 #37B50 #52C23 #54H20 #55N05 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Quasicrystal Structures and Properties #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1512.00398

openalex publication_date 2015/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a GUI fronted program that can compute combinatorial properties and topological invariants of recognisable and primitive symbolic substitutions on finite alphabets and their associated tiling spaces. We introduce theory from the study of aperiodic 1-dimensional tilings along with pseudocode highlighting the algorithms that we have implemented into the GUI. Grout is written using C++ and its standard library.

Citations

• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
• Pentaplexity A Class of Non-Periodic Tilings of the Plane

Related

• Finite-state transducers for substitution tilings
• Combinatorial substitutions and sofic tilings
• Matching Rules for the Sphinx Tiling Substitution
• Construction of fixed points of certain substitution systems by interlacing arrays in 1 and 2 dimensions
• Lots of Aperiodic Sets of Tiles