The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our thread, we adress the relation between the optical response and the associated complexity.