Disordered waves in the light-sensitive Belousov-Zhabotinsky reaction (``ripples,'' i.e., aperiodic wave front deformations, labyrinthine patterns, and ``frazzle gases,'' i.e., erratically moving wave fragments) were observed experimentally a few years ago, but have so far not been explained and modeled. The system, consisting of a gel with immobilized catalyst covered by a catalyst-free solution, is motionless and horizontally homogeneous. The observed disorder is related to enhancement or breakups of fluctuation valleys. In the model presented here, this destabilization is caused by inhibitor produced in the refractory tail that diffusively surpasses the wave front via the upper solution layer. This is in agreement with experiments both qualitatively, i.e., in the overall appearance of the patterns, as well as quantitatively, regarding the eikonal relationship and autocorrelation analysis.