Grout: A 1-Dimensional Substitution Tiling Space Program

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.