Twisting and stacking two copies of a 2D crystal can produce a long-wavelength periodic interference pattern known as a moir\'e pattern. Performing the same procedure with an aperiodic structure instead generates a single moir\'e spot at the rotation center, known as a Glass pattern. We explore the implications of these patterns across a variety of models: they allow measurement of microscopic parameters from mesoscopic resistivity measurements; they generate an impurity that modifies the properties of a moir\'e lattice at the rotation center; and they allow for domain formation in amorphous magnets. These results establish Glass patterns as a generic feature of twisted disordered systems and provide a framework for future theoretical and experimental exploration.