Using the haem group of myoglobin as a probe in optical experiments makes it possible to study its conformational fluctuations in real time. Results of these experiments can be directly interpreted in terms of the structure of the potential energy surface of the protein. The current view is that proteins have rough energy landscapes comprising a large number of minima which represent conformational substates, and that these substates are hierarchically organized. Here, we show that the energy landscape is characterized by a number of discrete distributions of barrier heights each representing a tier within a hierarchy of conformational substates. Furthermore, we provide evidence that the energy surface is self-similar and offer suggestions for a characterization of the protein fluctuations.