Aperiodic tiling

Abstract

These is an aesthetic pleasure when contemplating orderly structures that contain some disorder. A completely disordered pattern is typically not very interesting, but neither is a very regular one, like a check board. The check board and most images that we will meet in the following are examples of tessellations. A plane tessellation (or tiling) is a covering without gaps or overlaps, by figures called tiles. Tessellations can have very different degrees of order and disorder and illustrate well the concept expressed in the first statement.