I will present recent results obtained both theoretically and experimentally on fractal spectral properties of a polariton gas in a Fibonacci quasi-periodic potential. The observed spectrum is accurately reproduced from a theoretical model that we shall present. We have observed for the first time log-periodic oscillations and the opening of mini-gaps following the gap labeling theorem. These results illustrate the potential of cavity polaritons as a quantum simulator in complex topological geometries. | 
