Colouring monohedral tilings: defects and grain boundaries

TL;DR

This paper proves that certain periodic monohedral tilings with finite seed colors can enforce non-periodic coloring patterns across the entire plane, revealing complex behaviors in tiling colorings.

Contribution

It introduces the first proof that specific periodic monohedral tilings can generate non-periodic colorings of the plane from finite seeds.

Findings

Existence of periodic monohedral tilings with non-periodic colorings

Finite seeds can induce non-periodic coloring patterns

Implications for understanding tiling symmetry and coloring complexity

Abstract

In this paper it is proved that there exist periodic monohedral tilings and finite seeds of colored tiles, which force non-periodic coloring of the whole plane