A Frameless 2-Coloring of the Plane Lattice

Abstract

Summary A picture frame in two dimensions is a rectangular array of symbols, with at least two rows and columns, where the first and last rows are identical, and the first and last columns are identical. If a coloring of the plane lattice has no picture frames, we call it frameless. In this note, we show how to create a simple 2-coloring of the plane lattice that is frameless.