  We have recently shown [Blunt et al., Science 322, 1077 (2008)] that
p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles
into a two-dimensional rhombus random tiling. This tiling is close to ideal,
displaying long range correlations punctuated by sparse localised tiling
defects. In this paper we explore the analogy between dynamic arrest in this
type of random tilings and that of structural glasses. We show that the
structural relaxation of these systems is via the propagation--reaction of
tiling defects, giving rise to dynamic heterogeneity. We study the scaling
properties of the dynamics, and discuss connections with kinetically
constrained models of glasses.
