The influence of the environment on Lévy random search efficiency: Fractality and memory effects

► The efficiency of Lévy searches for the location of resources with fractal distribution is studied. ► Non-destructive searching is universal as regards spatial scaling of the target distribution. ► Destructive searching strongly depends on the degree of target aggregation. ► We also study how the memory and learning skills of the searcher affect the efficiency. ► Memory does not always increase the rate of target encounters in random searches.