The human brain is a highly complex system with nonlinear, dynamic behavior. A majority of brain imaging studies employing functional near-infrared spectroscopy (fNIRS), however, have considered only the spatial domain and have ignored the temporal properties of fNIRS recordings. Methods capable of revealing nonlinearities in fNIRS recordings can provide new insights about how the brain functions. The temporal characteristics of fNIRS signals are explored by comprehensively investigating their fractal properties. Fractality of fNIRS signals is analyzed using scaled windowed variance (SWV), as well as using visibility graph (VG), a method which converts a given time series into a graph. Additionally, the fractality of fNIRS signals obtained under resting-state and task-based conditions is compared, and the application of fractality in differentiating brain states is demonstrated for the first time via various classification approaches. Results from SWV analysis show the existence of high fractality in fNIRS recordings. It is shown that differences in the temporal characteristics of fNIRS signals related to task-based and resting-state conditions can be revealed via the VGs constructed for each case. fNIRS recordings, regardless of the experimental conditions, exhibit high fractality. Furthermore, VG-based metrics can be employed to differentiate rest and task-execution brain states.