The eye movements are closely related to information selection and attention allocation and depend on bottom-up and top-down processes. Previous research showed that the joint distributions of saccade amplitudes and directions are a sensitive measure of the effects of image type and content and the participant's age. We aimed to understand whether the task and the learning of the spatial regularities in images affect the relationship between the saccade amplitudes and directions. The stimuli consisted of pairs of patterns with 0, 1 or 2 coincident groupings of squares. The left pattern was in its original orientation and the right pattern was rotated at 90°, 180° or 270° to it. The stimuli lasted until the observer’s response but no longer than 3 s. The pattern repetitions varied from 12 to 96 times in one experiment with 180 trials. Nine observers participated in 3 experimental sessions. Observers’ task was to decide whether the patterns in the stimulus were the same or different. Eye movements were recorded during the experiments. Our results show: (1) substantial difference in the saccade-direction relationships from the typical biases observed in free viewing natural scenes; (2) changes in the joint distributions of the saccade amplitudes and directions in the process of learning; (3) difference in the angular distributions of the saccades depending on the response time. Our data expand previous research, showing that joint distributions also reflect the learning process of spatial regularities in the images.