  In this paper we study cellular automata (CAs) that perform the computational
Majority task. This task is a good example of what the phenomenon of emergence
in complex systems is. We take an interest in the reasons that make this
particular fitness landscape a difficult one. The first goal is to study the
landscape as such, and thus it is ideally independent from the actual
heuristics used to search the space. However, a second goal is to understand
the features a good search technique for this particular problem space should
possess. We statistically quantify in various ways the degree of difficulty of
searching this landscape. Due to neutrality, investigations based on sampling
techniques on the whole landscape are difficult to conduct. So, we go exploring
the landscape from the top. Although it has been proved that no CA can perform
the task perfectly, several efficient CAs for this task have been found.
Exploiting similarities between these CAs and symmetries in the landscape, we
define the Olympus landscape which is regarded as the ''heavenly home'' of the
best local optima known (blok). Then we measure several properties of this
subspace. Although it is easier to find relevant CAs in this subspace than in
the overall landscape, there are structural reasons that prevent a searcher
from finding overfitted CAs in the Olympus. Finally, we study dynamics and
performance of genetic algorithms on the Olympus in order to confirm our
analysis and to find efficient CAs for the Majority problem with low
computational cost.
