Multistable perception occurs when a single but ambiguous stimulus drives perceptual alternations. Understanding its mechanisms has a direct impact on perceptual inference and decision making. A model proposed by Shpiro and colleagues explains the dynamics of bistable perception through neural adaptation and driving noise. Eye movement data from an experiment, in which participants observed a moving Necker cube in a continuous viewing paradigm, revealed that micropursuit-like fixational eye movements (FEM) can occur; a type of movements not accounted for in current FEM models. Our analysis also suggested that FEM can have an influence on adaptation and noise (Parisot et al., ECEM'17, Hicheur et al., JOV'13). Therefore, we propose a model that could help predict and explain away interactions between FEM and multistablity dynamics. It is based on gravity potential fields where their distortion by attractors allows the generation of multistability for the position of the gaze w.r.t. the different attractors. Adaptation and noise can be used as mechanisms to simulate the impact of stimulus motion and the task on FEM. Perceptual memory and/or anticipation of stimulus motion can be taken into account through potential field distortion. The model is able to generate drift, tremor, microsaccades, and micropursuits, showing that stimulus motion can influence the trajectories of drifts and microsaccades. Using attractors provides a link between models of multistable perception and FEM based on the mechanisms of noise and adaptation; making it possible to find correlations between perceptual and oculomotor dynamics.