Deltoid Tangents with Evenly Distributed Orientations and Random Tilings

Abstract

We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained a sa result of tile rearrangements in the substitution rules associated to edge flips. Special types of random tilings for Euclidean, spherical and hyperbolic three-manifolds are also considered.