Crossings: flying over antisymmetric Truchet friezes

Abstract

Symmetry and antisymmetry are resources used by humans since pre-historic times in their artistic creations. In this work we start by introducing antisymmetry and the 17 possible associated groups. We then present some counts of friezes, built with a particular module, the Truchet tile, which is itself antisymmetric. These counts take into consideration the frieze antisymmetry group and the number of tiles composing the unitary cell which originates the frieze by translation. These Truchet friezes led to the creation of a set of 5 paintings, named Crossings, which illustrate all the possible groups, in an artistic context.