The receptive field (RF) of neurons recorded from the lateral intraparietal area (LIP) was quantified using a rapid, computer-driven mapping procedure. For each neuron, the RF was mapped: (1) during attentive fixation and (2) during free visual exploration. RF location, size and internal structure were modulated by the mapping context in over two-thirds of the recorded neurons. The major trend was a proportionally larger amount of neuronal visual resources allocated to central space during fixation, and an attenuated center-to-periphery gradient in the visual field representation during free gaze. A population approach shows that these spatial modulations are accompanied by changes in the signal-to-noise ratio of the information carried in the RF substructure. We related these neurophysiological observations to behavior, by comparing the characteristics of saccades elicited during fixation and free gaze. Together, the results suggest that the dynamics of LIP visual RFs may characterize both the state of engagement of attention and the power of resolution of visual analysis: during fixation, the neural population is locked in a filter state concentrating the processing resources at the fovea, while during free gaze, the population shifts to a detector state spreading the resources more evenly across the visual field.