  Periodic and disordered media are known to possess different transport
properties, either classically or quantum-mechanically. This has been exhibited
by effects such as Anderson localization in systems with disorder and the
existence of photonic bandgaps in the periodic case. In this paper we analyze
the transport properties of disordered waveguides with corners at very low
frequencies, finding that the spectrum, conductance and wavefunctions are
immune to disorder. Our waveguides are constructed by means of randomly
oriented straight segments and connected by corners at right angles. Taking
advantage of a trapping effect that manifests in the corner of a bent
waveguide, we can show that a tight-binding approximation describes the system
reasonably well for any degree of disorder. This provides a wide set of
non-periodic geometries that preserve all the interesting transport properties
of periodic media.
