The structure of thin, wavy falling films was studied to evaluate whether the random‐appearing wave structure is a result of deterministic chaos or a purely stochastic process. The time‐varying film thickness was obtained at different spatial locations near the point of wave inception for flow rates in the range of Re=3–10. Under all conditions the wave structure was aperiodic in nature and displayed none of the known transitions to chaos. However, the power spectra followed an exponential decay law at high frequencies that is characteristic of chaotic systems. The estimated attractor dimension, used to characterize the complexity of a chaotic system, was much higher than those of known model chaotic systems. It is demonstrated that these high values could be explained due to small levels of noise present in experimental situations. Since experimental data are seldom noise free, a basic limitation in applying these methods to experimental measurements is demonstrated.