Grout: A 1-Dimensional Substitution Tiling Space Program
Scott Balchin, Dan Rust
TL;DR
Grout is a C++ GUI program that computes combinatorial and topological properties of 1D symbolic substitution tilings, integrating theoretical algorithms for analyzing aperiodic tilings.
Contribution
It provides a user-friendly tool that implements algorithms from aperiodic tiling theory to analyze substitution tilings and their invariants.
Findings
Successfully computes properties of 1D substitution tilings
Integrates theoretical algorithms into a practical GUI tool
Facilitates research in aperiodic tilings
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.
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Taxonomy
TopicsQuasicrystal Structures and Properties · semigroups and automata theory · Cellular Automata and Applications