Dimensional complexity (DCx) is an EEG measure derived from nonlinear systems theory that can be indicative of the global dynamical complexity of electrocortical activity. This study examined developmental changes in DCx, as well as the effects of cognitive tasks, gender, and brain topography, and compared DCx with traditional spectral power measures. EEG was recorded in three groups of children at mean age of 7.5 (n = 37), 13.8 (n = 42), and 16.4 (n = 56) years at rest and during the performance of verbal and spatial cognitive tasks. DCx measured both at rest and during tasks increased with age. Specific effects of brain topography, condition, and gender became stronger with age, suggesting an increase in structural and functional differentiation of the cortex. Hemispheric asymmetry of DCx recorded during tasks also increased with age, with the task-induced DCx reduction being stronger in the left hemisphere. Gender differences in DCx suggested faster cerebral maturation in girls over late adolescence. Relationships between DCx and spectral power varied as a function of tasks and scalp locations, suggesting that these EEG measures can reflect different aspects of cortical functioning.