Quantum wells with fractal-like interfaces arise in the growth of semiconductor heterostructures. Such fractal characteristics largely influence the optical and transport properties in these constrained geometries. We report a systematic study of growth through the study of optical properties. The spectra obtained show "anomalous behavior", whose characteristics depends on the growth procedure. The theoretical analysis was performed resorting to an unconventional statistical-mechanical formalism. It allows one to correlate growth conditions with surface roughness, and to determine their influence on experimental results, allowing one to obtain a picture of the physics involved in such systems.181217431758