In many complex systems control situations, searching for solutions or alternatives is involved. Searching for solutions can be modeled by a search on a fitness landscape. Knowing the structure of the underlying landscape can help in explaining or predicting aspects of an actual seach on it, and thus in controlling the system that is living on the landscape. <p> This paper presents results on characterizing the structure of the fitness landscape that results from searching for a cellular automaton, a simple mathematical model of a complex system, that can perform a certain non-trivial computational task (global synchronization). The structure of this landscape turns out to be quite different from the more standard fitness landscapes that have been looked at so far. It is furthermore shown that the characterization of this structure can explain certain phenomena that are observed in an actual search on this landscape.
