  Identity-homotopic self-homeomorphisms of a space of non-periodic
1-dimensional tiling are generalizations of orientation-preserving
self-homeomorphisms of circles. We define the analogue of rotation numbers for
such maps. In constrast to the classical situation, additional assumptions are
required to make rotation numbers globally well-defined and independent of
initial conditions. We prove that these conditions are sufficient, and provide
counterexamples when these conditions are not met.
