  In olfactory search an immobile target emits chemical molecules at constant
rate. The molecules are transported by the medium which is assumed to be
turbulent. Considering a searcher able to detect such chemical signals and
whose motion follows the infotaxis strategy, we study the statistics of the
first-passage time to the target when the searcher moves on a finite
two-dimensional lattice of different geometries. Far from the target, where the
concentration of chemicals is low the direction of the searcher's first
movement is determined by the geometry of the domain and the topology of the
lattice, inducing strong fluctuations on the average search time with respect
to the initial position of the searcher. The domain is partitioned in well
defined regions characterized by the direction of the first movement. If the
search starts over the interface between two different regions, large
fluctuations in the search time are observed.
