When ambiguous visual stimuli are presented continuously, they often lead to oscillations between usually two perceptions. Because of these oscillations, it has been thought that the underlying neural dynamics also arises from a binary or two-state system. Contradicting the binary assumption, it has been shown recently that the perception of some ambiguous stimuli is governed by continuously varying internal states, measured as biases that differ considerably from one observer to the next and that can also evolve over time (Wexler, Duyck, & Mamassian, 2015). Here I study bias patterns in the motion quartet, an ambiguous apparent motion stimulus, as the quartet's orientation is varied. The bias patterns are robustly idiosyncratic, and are even more complex than those that have been described previously. There are two qualitatively different bias types: Some observers prefer a translation axis, while others show preference for a rotation direction. Each type also varies parametrically: the orientation of the preferred axis, and the direction of preferred rotation. There are also clear cases of combination of the two bias types. When measured repeatedly over 9 hr, the bias patterns usually remain stable, but also sometimes evolve both parametrically (e.g., change of preferred axis), as well as across bias type (change from axial to rotational bias). Control experiments revealed that the variety of bias patterns observed across subjects, and their changes over time, are not due to voluntary decisions. Overall, these results exhibit the multidimensional complexity of internal states underlying the perception of even simple stimuli.