Tiling with Small Tiles

TL;DR

This paper investigates sets of small tiles capable of covering any large enough square grid region, introduces a related tiling problem, and provides results on domino and L-shape tile tilings, contributing to tiling theory.

Contribution

It introduces new tile sets for universal tiling of large regions and connects these findings to classic tiling problems with dominoes and L-shapes.

Findings

Identifies tile sets that can tile any region larger than size 1

Provides a new approach to classic domino and L-shape tiling problems

Demonstrates how these results can aid in solving other tiling challenges

Abstract

We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems -- we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.