Eye movements gather visual information from the environment for various purposes and goals. Spatial patterns of eye movements vary depending on the layout of visual information, and intentions of the observer. However, despite this variability, basic principles of visual information gathering may be reflected in lawful properties of eye movement trajectories that hold across various stimulus and intentional conditions. Two experiments are presented analyzing eye movement trajectories during scene perception across pictures with varying spatial frequency distributions (Expt 1), and across two different task conditions, "finding" versus "counting" tasks (Expt 2). Results show that, in all conditions, distributions of saccade amplitudes are heavy-tailed and nearly identical in shape, and fixation fluctuation series are long-range correlated with nearly identical spectral slopes. While a small effect of task intention was found, the broader conclusion is that eye movements during scene perception exhibit general statistical characteristics that models have yet to address.