Seemingly conflicting phenomena of segregation and integration have been observed both in the immune system and the neural system, and possible mechanisms have been studied relating to learning and adaptation. Inspired by the stable marriage problem whose solutions may exhibit both segregation and integration among agents, we propose a working model of matching automata which take order of preference as inputs and the resultant matching among agents as outputs. In this tentative model, we try to simulate the integration taking the switching experienced in the Necker Cube as an example, while the segregation is built into the restrictions of the model.