Topological Mixing Tilings of $\mathbb{R}^2$ Generated by a Generalized Substitution

Abstract: Kenyon, in his 1996 paper, gave a class of examples of tilings of \mathbb{R}^2 constructed from generalized substitutions. These examples are topologically conjugate to self-similar tilings of the plane (with fractal boundaries). I have proven that an infinite sub-family of Kenyon's examples are topologically mixing. These are the first known examples of topologically mixing substitution tiling dynamical systems of \mathbb{R^2}.