Escher degree of non-periodic L-tilings by 2 prototiles

TL;DR

This paper introduces the concept of escher degree to quantify the flexibility of non-periodic L-tilings by two prototiles, analyzing their edge perturbation degrees.

Contribution

It determines the escher degree for non-periodic L-tilings with two prototiles, providing new insights into their geometric flexibility.

Findings

Escher degree quantifies edge perturbation flexibility.

Non-periodic L-tilings by 2 prototiles have specific escher degrees.

The study advances understanding of tiling deformation properties.

Abstract

For a given tiling of the euclidean plane ${\bf E}^2$, we call the degree of freedom of perturbed edges of prototiles {\it escher degree}. In this paper we consider non-periodic L-tilings by 2 prototiles and obtain the escher degree of them.